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Gaudin model modulo p, Tango structures, and dormant Miura opers J. Geometr. Phys. (IF 1.5) Pub Date : 2024-03-20 Yasuhiro Wakabayashi
In the present paper, we study the Bethe ansatz equations for Gaudin model and Miura opers in characteristic . Our study is based on a work by E. Frenkel, in which solutions to the Bethe ansatz equations are described in terms of Miura opers on the complex projective line. The main result of the present paper provides a positive characteristic analogue of this description. We pay particular attention
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Taut almost cosymplectic hyperbolas and almost bi-contact metric structures on three-manifolds J. Geometr. Phys. (IF 1.5) Pub Date : 2024-03-18 Domenico Perrone
Cappelletti-Montano et al. introduced and studied taut cosymplectic circles/spheres, which are the analogues in the cosymplectic setting of taut contact circles/spheres introduced and studied by Geiges-Gonzalo , , . The main purpose of this paper is to introduce and study, in dimension three, the hyperbolic analogue in the cosymplectic setting. We give a characterization of a taut almost cosymplectic
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On anti-quasi-Sasakian manifolds of maximal rank J. Geometr. Phys. (IF 1.5) Pub Date : 2024-03-16 Dario Di Pinto
We discuss the existence of invariant anti-quasi-Sasakian (aqS) structures of maximal rank on compact homogeneous Riemannian manifolds and on nilpotent Lie groups. In the former case we obtain a non-existence result, while in the latter case we provide a complete classification. We also show that every compact aqS manifold has nonvanishing second Betti number.
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3d super hyperbolic geometry J. Geometr. Phys. (IF 1.5) Pub Date : 2024-03-12 Robert Penner
Wigner's unitary representation of the Lorentz group is extended to a representation of the complex orthosymplectic Lie super group acting on Minkowski (3,1|4)-dimensional super space essentially by Hermitean conjugation. The invariant quadratic form is in Wigner's coordinates and , where are Dirac fermions. The extended action is linear in the super space variables, but not quadratic in the odd group
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Integrable geodesic flows and metrisable second-order ordinary differential equations J. Geometr. Phys. (IF 1.5) Pub Date : 2024-03-08 Sergei V. Agapov, Maria V. Demina
It is well known that the system of ordinary differential equations (ODEs) describing geodesic flows of some Riemannian metrics on 2-surfaces admits a projection on a special class of second-order ODEs. In this paper we study in detail this special class of ODEs. We classify all such autonomous ODEs possessing autonomous first integrals that are fractional-quadratic in the first derivative. We construct
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Vertical isomorphisms of Fedosov dg manifolds associated with a Lie pair J. Geometr. Phys. (IF 1.5) Pub Date : 2024-03-08 Hua-Shin Chang, Hsuan-Yi Liao
We investigate vertical isomorphisms of Fedosov dg manifolds associated with a Lie pair , i.e. a pair of a Lie algebroid and a Lie subalgebroid of . The construction of Fedosov dg manifolds involves a choice of a splitting and a connection. We prove that, given any two choices of a splitting and a connection, there exists a unique vertical isomorphism, determined by an iteration formula, between the
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Chaotic foliations with Ehresmann connection J. Geometr. Phys. (IF 1.5) Pub Date : 2024-03-08 Nina I. Zhukova
We consider smooth codimension foliations on -dimensional manifolds where . We use Ehresmann connections as a technical tool to introduce the notion of sensitivity to initial conditions for foliations. We extend Devaney's definition of chaos for cascades to foliations with Ehresmann connection. Our main result states that sensitivity to initial conditions of a foliation with Ehresmann connection follows
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Decay estimate for Yang-Mills fields on ALE spaces and applications J. Geometr. Phys. (IF 1.5) Pub Date : 2024-03-07 Youmin Chen, Miaomiao Zhu
We study the decay estimates at the infinity for Yang-Mills connections on Ricci flat ALE manifolds and explore some applications.
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A generalized super Camassa-Holm equation J. Geometr. Phys. (IF 1.5) Pub Date : 2024-03-07 Nianhua Li, Kai Tian
We propose a generalized super Camassa-Holm equation, which is completely integrable in the sense of admitting of a Lax pair and a bi-Hamiltonian structure. Through Dirac reduction, we obtain a bi-Hamiltonian structure of the super Camassa-Holm equation introduced by Geng, Xue and Wu [Stud. Appl. Math. (2013) 1-16]. By introducing an appropriate reciprocal transformation, we connect the generalized
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Oxidation, reduction and semi-classical limit for quantum matrix geometries J. Geometr. Phys. (IF 1.5) Pub Date : 2024-03-04 Laura O. Felder, Harold C. Steinacker
Matrix configurations define noncommutative spaces endowed with extra structure including a generalized Laplace operator, and hence a metric structure. Made dynamical via matrix models, they describe rich physical systems including noncommutative gauge theory and emergent gravity. Refining the construction in , we construct a semi-classical limit through an immersed submanifold of complex projective
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Mirror map for Landau-Ginzburg models with nonabelian groups J. Geometr. Phys. (IF 1.5) Pub Date : 2024-03-01 Annabelle Clawson, Drew Johnson, Duncan Morais, Nathan Priddis, Caroline B. White
BHK mirror symmetry as introduced by Berglund–Hübsch and Marc Krawitz between Landau–Ginzburg (LG) models has been the topic of much study in recent years. An LG model is determined by a potential function and a group of symmetries. BHK mirror symmetry is only valid when the group of symmetries is comprised of the so-called diagonal symmetries. Recently, an extension to BHK mirror symmetry to include
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Flat coordinates of algebraic Frobenius manifolds in small dimensions J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-29 Misha Feigin, Daniele Valeri, Johan Wright
Orbit spaces of the reflection representation of finite irreducible Coxeter groups provide polynomial Frobenius manifolds. Flat coordinates of the Frobenius manifold metric are Saito polynomials which are distinguished basic invariants of the Coxeter group.
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On the stability of T-space forms J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-29 C, r, i, n, a, , D, a, n, i, e, l, a, , N, e, a, c, ş, u
The stability property of harmonic mappings plays a fundamental role in both mechanics and mathematical physics. This work is devoted to the investigation of the stability property on -space forms, i.e. -manifolds of constant -sectional curvature. According to Blair (1970) , -manifolds along with -manifolds and -manifolds represent the three important classes of manifolds with structural groups . Using
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Virtual Euler characteristics via topological recursion J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-28 L, e, o, n, i, d, , O, ., , C, h, e, k, h, o, v
We use Seiberg–Witten-like relations in the topological recursion framework to obtain virtual Euler characteristics for uni- and multicellular maps for ensembles of classic orthogonal polynomials and for ensembles related to nonorientable surfaces. We also discuss Harer–Zagier-type recursion relations for 1-point correlation function for the Legendre ensemble.
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Topology of Hankel matrices and applications J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-27 Eman Ahmad, Cenap Ozel, Selcuk Koyuncu
In this paper we first construct a Lie group structure on Hankel matrices over by Hadamard product and then we find its Lie algebra structure and finally calculate dimension of this manifold over . Moreover, we discuss topological properties of this manifold using Frobenious norm. We pointed out the relation between Lie group and Lie algebra structures of these matrices by exponential map. It is also
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A note on the Gromov width of toric manifolds J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-23 Narasimha Chary Bonala, Stéphanie Cupit-Foutou
The Gromov width of a uniruled projective Kähler manifold can be bounded from above by the symplectic area of its minimal curves. We apply this result to toric varieties and thus get in this case upper bounds expressed in toric combinatorial invariants.
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A quadric ansatz method for a certain class of second order PDEs J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-22 Prim Plansangkate
We develop a procedure to implement the method of quadric ansatz to a class of second order partial differential equations (PDEs), which includes the four-dimensional Kähler-Einstein equation with symmetry and the one-sided type-D Einstein equation with nonzero scalar curvature. The procedure, which reduces the PDEs to ordinary differential equations (ODEs), involves imposing additional constraints
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Equivariant cohomology and deformation for algebras - an operadic approach J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-22 Xuan Yu
Let be an operad with a multiplication, and later with a (higher) derivation. This paper introduces and develops a notion of (partial) group action and corresponding equivariant cohomology and deformation theory on . It generalizes existing results for equivariant cohomology and deformation for associative algebras, dialgebras, and dendriform algebras, among others. At the end, we discuss compatibilities
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Quasi-triangular pre-Lie bialgebras, factorizable pre-Lie bialgebras and Rota-Baxter pre-Lie algebras J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-22 You Wang, Chengming Bai, Jiefeng Liu, Yunhe Sheng
In this paper, first we introduce the notions of quasi-triangular pre-Lie bialgebras and factorizable pre-Lie bialgebras. A factorizable pre-Lie bialgebra leads to a factorization of the underlying pre-Lie algebra. We show that the symplectic double of a pre-Lie bialgebra naturally enjoys a factorizable pre-Lie bialgebra structure. Then we give the Rota-Baxter characterization of factorizable pre-Lie
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Noncommutative Riemannian geometry of Kronecker algebras J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-20 Joakim Arnlind
We study aspects of noncommutative Riemannian geometry of the path algebra arising from the Kronecker quiver with arrows. To start with, the framework of derivation based differential calculi is recalled together with a discussion on metrics and bimodule connections compatible with the ⁎-structure of the algebra. As an illustration, these concepts are applied to the noncommutative torus where examples
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Geometric inequalities of bi-warped product submanifold in generalized complex space form J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-20 Sachin Kumar Srivastava, Anuj Kumar
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Internal Lagrangians of PDEs as variational principles J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-20 Kostya Druzhkov
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Nearly trans-Sasakian manifolds of constant holomorphic sectional curvature J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-19 Aligadzhi Rabadanovich Rustanov, Svetlana Vladimirovna Kharitonova
The geometry of nearly trans-Sasakian manifolds of constant holomorphic sectional curvature is studied in this paper. It is proved that a harmonic nearly trans-Sasakian Einstein manifold is a manifold of non-positive scalar curvature, and, in the case of zero scalar curvature, it is locally equivalent to the product of a Ricci-flat nearly Kählerian manifold and the real line. Expressions for the Riemannian
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Courant-Dorfman algebras of differential operators and Dorfman connections of Courant algebroids J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-19 Panagiotis Batakidis, Fani Petalidou
We construct an algebra and a complex of multidifferential operators on tensor products of a Courant algebroid with values in the endomorphism bundle of a smooth vector bundle , predual of , extending the standard complex of the Courant-Dorfman algebra of . Also, we study Dorfman connections of on , and show that the Cartan calculus, curvatures of induced connections and basic differential geometric
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Timelike surfaces in N×R with a canonical null direction J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-19 Gabriel Ruiz-Hernández, Fernando Valdez-Ortega
Let be a Lorentz surface and let be a unit vector field on the Lorentz manifold tangent to . A timelike surface Σ in is said to have a canonical null direction with respect to if the projection on the tangent space of Σ gives a lightlike vector field. We prove that these surfaces are minimal and ruled, whose rulings are lightlike geodesics and lines of curvature. Other results include the fact that
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About the 2-cohomology of the Orthosymplectic superalgebra J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-15 Olfa Messaoud
Let be the -module of weighted densities on of weight . We compute the second cohomology spaces . We explicitly give cocycles spanning these cohomology spaces. This work is the simplest generalization of a result by Basdouri and Sayari (2011) .
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Metric-Bourbaki algebroids: Cartan calculus for M-theory J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-15 Aybike Çatal-Özer, Tekin Dereli, Keremcan Doğan
String and M theories seem to require generalizations of usual notions of differential geometry on smooth manifolds. Such generalizations usually involve extending the tangent bundle to larger vector bundles equipped with various algebroid structures such as Courant algebroids, higher Courant algebroids, metric algebroids, or -algebroids. The most general geometric scheme is not well understood yet
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Dimensional curvature identities in Fedosov geometry J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-08 Adrián Gordillo-Merino, Raúl Martínez-Bohórquez, José Navarro-Garmendia
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Riesz means and bilinear Riesz means on H-type groups J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-08 Min Wang, Yingzhan Wang
In this paper, we investigate the Riesz means and the bilinear Riesz means associated to the sublaplacian on H-type groups. We obtain the -boundedness of by using the restriction theorem on H-type groups. Our result is different from that on Heisenberg groups. We prove that is bounded from into for and when is larger than a suitable smoothness index . Because we consider H-type groups with the center
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Riemannian foliations and geometric quantization J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-07 Yi Lin, Yiannis Loizides, Reyer Sjamaar, Yanli Song
We introduce geometric quantization for constant rank presymplectic structures with Riemannian null foliation and compact leaf closure space. We prove a quantization-commutes-with-reduction theorem in this context. Examples related to symplectic toric quasi-folds, suspensions of isometric actions of discrete groups, and K-contact manifolds are discussed.
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Complex geometry and Hermitian metrics on the product of two Sasakian manifolds J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-07 Vlad Marchidanu
A Sasakian manifold is a Riemannian manifold whose metric cone admits a certain Kähler structure which behaves well under homotheties. We show that the product of two compact Sasakian manifolds admits a family of complex structures indexed by a complex nonreal parameter, none of whose members admits either compatible Kähler metrics, locally conformally Kähler metrics or balanced metrics, if both Sasakian
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Differential mock-Lie bialgebras and admissible mock-Lie Yang-Baxter equations J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-07 Ismail Laraiedh
The purpose of this paper is to introduce the notion of differential mock-Lie bialgebra. Also, the admissibility of a linear operator is defined in order to construct a reasonable representation on the dual space. Explicitly, differential mock-Lie bialgebras are characterized by generalizing matched pairs and Manin triples of differential mock-Lie algebras. Additionally, the admissible mock-Lie Yang-Baxter
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On flat elliptic centroaffine Tchebychev hypersurfaces J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-02 Qian Zhao, Xiuxiu Cheng, Zejun Hu
In this paper, studying locally strongly convex flat elliptic centroaffine hypersurfaces in , we first give a centroaffine geometric characterization of the hypersurface . Then, restricted to , we establish the classification of flat elliptic centroaffine Tchebychev hypersurfaces in . The latter is an extension of the result of Lalléchère et al. (2021) which classified flat hyperbolic centroaffine
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Harmonic morphisms on Lie groups and minimal conformal foliations of codimension two J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-02 Sigmundur Gudmundsson, Thomas Jack Munn
Let be a Lie group equipped with a left-invariant semi-Riemannian metric. Let be a semisimple subgroup of generating a left-invariant conformal foliation of codimension two on . We then show that the foliation is minimal. This means that locally the leaves of are fibres of a complex-valued harmonic morphism. In the Riemannian case, we prove that if the metric restricted to is biinvariant then is totally
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On classification of irreducible conformal B(p)-modules of finite rank J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-02 Jianzhi Han, Yumeng Zhan
The classification of irreducible conformal -modules of finite rank was given in for and in for . In this paper, we use a uniform way to give a short proof of this classification.
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Free post-groups, post-groups from group actions, and post-Lie algebras J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-01 Mahdi Jasim Hasan Al-Kaabi, Kurusch Ebrahimi-Fard, Dominique Manchon
After providing a short review on the recently introduced notion of post-group by Bai, Guo, Sheng and Tang, we exhibit post-group counterparts of important post-Lie algebras in the literature, including the infinite-dimensional post-Lie algebra of Lie group integrators. The notion of free post-group is examined, and a group isomorphism between the two group structures associated to a free post-group
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Quantum K theory rings of partial flag manifolds J. Geometr. Phys. (IF 1.5) Pub Date : 2024-02-01 Wei Gu, Leonardo Mihalcea, Eric Sharpe, Weihong Xu, Hao Zhang, Hao Zou
In this paper we use three-dimensional gauged linear sigma models to make physical predictions for Whitney-type presentations of equivariant quantum K theory rings of partial flag manifolds, as quantum products of universal subbundles and various ratios, extending previous work for Grassmannians. Physically, these arise as OPEs of Wilson lines for certain Chern-Simons levels. We also include a simplified
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The virtual intersection theory of isotropic Quot Schemes J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-30 Shubham Sinha
Isotropic Quot schemes parameterize rank r isotropic subsheaves of a vector bundle equipped with symplectic or symmetric quadratic form. We define a virtual fundamental class for isotropic Quot schemes over smooth projective curves. Using torus localization, we prescribe a way to calculate top intersection numbers of tautological classes, and obtain explicit formulas when r=2. These include and generalize
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Bi-Hamiltonian structure of a unit geodesic vector field on a 3D space of constant negative curvature J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-24 T. Bayrakdar
In this work we consider the Riemannian manifold defined by the product of an integral curve of a Cauchy-Riemann vector field on the Poincaré upper half-plane and its image in the tangent bundle. We show that for a Cauchy-Riemann vector field the Chern-Simons three-form identically vanishes and for the Killing vector field X=x∂x+y∂y the manifold is a space of constant negative curvature. We also show
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A detailed description of the generalized Calabi type Kähler surfaces J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-22 Ewelina Mulawa
In this paper we study 4-dimensional Riemannian manifolds admitting a Kähler complex structure with quasi-constant holomorphic sectional curvature, i.e., QCH Kähler surfaces. We give a detailed description of QCH Kähler surfaces of generalized Calabi type.
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A note on the geometry of the two-body problem on S2 J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-23 Alessandro Arsie, Nataliya A. Balabanova
Leveraging on the results of [7], we carry out an investigation of the algebraic three-fold ΣC,h, the common level set of the Hamiltonian and the Casimir, for the two-body problem for equal masses on S2 subject to a gravitational potential of cotangent type. We determine the topology of its compactification Σ‾C,h and how it bifurcates with respect to the admissible values of (C,h), (C being the fixed
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A new perspective on nonholonomic brackets and Hamilton–Jacobi theory J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-24 Manuel de León, Manuel Lainz, Asier López-Gordón, Juan Carlos Marrero
The nonholonomic dynamics can be described by the so-called nonholonomic bracket on the constrained submanifold, which is a non-integrable modification of the Poisson bracket of the ambient space, in this case, of the canonical bracket on the cotangent bundle of the configuration manifold. This bracket was defined in [6], [21] although there was already some particular and less direct definition. On
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Stratified vector bundles: Examples and constructions J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-24 Ethan Ross
A stratified space is a kind of topological space together with a partition into smooth manifolds. These kinds of spaces naturally arise in the study of singular algebraic varieties, symplectic reduction, and differentiable stacks. In this paper, we introduce a particular class of stratified spaces called stratified vector bundles, and provide an alternate characterization in terms of monoid actions
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Conformal pointwise slant Riemannian maps from or to Kähler manifolds J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-23 Adeeba Zaidi, Gauree Shanker, Jyoti Yadav
In this article, we study Conformal pointwise-slant Riemannian maps (CPSRM) from or to Kähler manifolds to or from Riemannian manifolds. To check the existence of such maps, we provide some non-trivial examples. We derive some important results for these maps. We discuss the integrability and totally geodesicness of the distributions. Further, we investigate the conditions for homotheticity and harmonicity
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Finsler surfaces with vanishing T-tensor J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-19 S.G. Elgendi
In this paper, for Finsler surfaces, we prove that the T-condition and σT-condition coincide. For higher dimensions n≥3, we illustrate by an example that the T-condition and σT-condition are not equivalent. We show that the non-homothetic conformal change of a Berwald (resp. a Landsberg) surface is Berwaldian (resp. Landsbergian) if and only if the σT-condition is satisfied. By solving the Landsberg's
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Totally geodesic and parallel hypersurfaces of Gödel-type spacetimes J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-18 Giovanni Calvaruso, Lorenzo Pellegrino, Joeri Van der Veken
We classify parallel and totally geodesic hypersurfaces of the relevant class of Gödel-type spacetimes, with particular regard to the homogeneous examples.
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Curvature and stability of quasi-geostrophic motion J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-18 Ali Suri
This paper outlines the study of the curvature of the quantomorphism group and its central extension, as well as the quasi-geostrophic equation. By utilizing spherical harmonics and structure constants, a formula for computing the curvature of the L2 metric on the central extension gˆ=g⋉ΩR is derived, where g represents the Lie algebra of Dμs(S2). The sectional curvatures of the planes containing Y10
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Complete lagrangian self-expanders in C2 J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-17 Zhi Li, Guoxin Wei
In this paper, we obtain a classification theorem of 2-dimensional complete Lagrangian self-expanders with constant squared norm of the second fundamental form in C2.
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Charged decoupled anisotropic spheres in f(R,T2) gravity J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-17 M. Sharif, Saba Naz
The main aim of this article is to examine the impact of charge on decoupled anisotropic spherical solutions in the energy-momentum squared gravity. We assume a sphere with two sources (seed and additional) and only alter the radial metric component. This divides the equations of motion into two arrays, one indicates an isotropic and another anisotropic source. The additional source with the isotropic
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Tangent functor on microformal morphisms, and non-linear pullbacks for forms and cohomology J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-11 Theodore Th. Voronov
We show how the tangent functor extends from ordinary smooth maps to “microformal morphisms” (also called “thick morphisms”) of supermanifolds. Microformal morphisms generalize ordinary maps and correspond to formal canonical relations between the cotangent bundles specified by generating functions depending on position variables on the source manifold and momentum variables on the target manifold
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The 4-fold Pandharipande–Thomas vertex J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-12 Henry Liu
We give a conjectural but full and explicit description of the (K-theoretic) equivariant vertex for Pandharipande–Thomas stable pairs on toric Calabi–Yau 4-folds, by identifying torus-fixed loci as certain quiver Grassmannians and prescribing a canonical half of the tangent-obstruction theory. For any number of non-trivial legs, the DT/PT vertex correspondence can then be verified by computer in low
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Algebraic cones of LCK manifolds with potential J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-12 Liviu Ornea, Misha Verbitsky
A complex manifold X, dimX>2, is called “an LCK manifold with potential”, if it can be realized as a complex submanifold of a Hopf manifold. Let X˜ be its Z-covering, considered as a complex submanifold in Cn﹨0. We prove that X˜ is algebraic. We call the manifolds obtained this way the algebraic cones, and show that the affine algebraic structure on X˜ is independent from the choice of X. We give several
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Deformation Theory of Asymptotically Conical Spin(7)-Instantons J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-11 Tathagata Ghosh
We develop the deformation theory of instantons on asymptotically conical Spin(7)-manifolds where the instanton is asymptotic to a fixed nearly G2-instanton at infinity. By relating the deformation complex with spinors, we identify the space of infinitesimal deformations with the kernel of the twisted negative Dirac operator on the asymptotically conical Spin(7)-manifold. Finally we apply this theory
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Prescription of finite Dirichlet eigenvalues and area on surface with boundary J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-11 Xiang He
In the present paper, we consider Dirichlet Laplacian on compact surface. We show that for a fixed surface with boundary X, a finite increasing sequence of real numbers 0
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Invariants of magnetic lines for Yang-Mills solutions J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-10 P.M. Akhmet'ev, M.S. Dvornikov
We construct a new Yang-Mills 3D-solution on the space of negative scalar curvature. We discuss a problem of non-abelian gauge symmetry is broken with the assumption that a scalar curvature of the domain is a negative small parameter. In this case we use the following fact: a geometrical scale related with Vassiliev's discriminant of magnetic lines coincides with a phisical Kolmogorov scale. This gives
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On the Poisson structure and action-angle variables for the Fokas-Lenells equation J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-08 Yun-Zhi Gao, Shou-Fu Tian, Hai-Ning Fan
In this paper, we employ the inverse scattering transform to investigate the action-angle variables of the Fokas-Lenells equation. Firstly, the Fokas-Lenells equation is derived by the variational principle, and the definition of the Poisson structure is presented. Then, the Poisson brackets between the scattering data are successfully determined by introducing the matrix tensor product. Thus the action-angle
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Coadjoint orbits of vortex sheets in ideal fluids J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-08 François Gay-Balmaz, Cornelia Vizman
We describe coadjoint orbits associated to the motion of codimension one singular vorticities in ideal fluids, e.g. vortex sheets in 3D. We show that these coadjoint orbits can be identified with a certain class of decorated nonlinear Grassmannians, that consist of codimension one submanifolds belonging to an isodrast (i.e., enclosing a given volume, provided their homology class vanishes), endowed
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Spectral properties of weighted Cauchy singular integral transform on S-poly-Barmgann spaces J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-08 Abdelatif Elkachkouri, Allal Ghanmi
We investigate some spectral properties of the weighted quaternionic Cauchy transform when acting on the right quaternionic Hilbert space of Gaussian integrable functions. We study its boundedness, compactness, and memberships to the k-Schatten class, and we identify its range. This is done by means of its restriction to the n-th S-polyregular Bargmann space of the second kind, for which we provide
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Port-Hamiltonian formulations of the incompressible Euler equations with a free surface J. Geometr. Phys. (IF 1.5) Pub Date : 2024-01-06 Xiaoyu Cheng, J.J.W. Van der Vegt, Yan Xu, H.J. Zwart
In this paper, we present port-Hamiltonian formulations of the incompressible Euler equations with a free surface governed by surface tension and gravity forces, modelling e.g. capillary and gravity waves and the evolution of droplets in air. Three sets of variables are considered, namely (v,Σ), (η,ϕ∂,Σ) and (ω,ϕ∂,Σ), with v the velocity, η the solenoidal velocity, ϕ∂ a potential, ω the vorticity,