Abstract
We find geodesics, shortest arcs, cut loci, and first conjugate loci for some left-invariant sub-Riemannian metrics on the Lie groups \( \operatorname{SU}(1,1)\times 𝕉 \) and \( \operatorname{SO}_{0}(2,1)\times 𝕉 \).
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Acknowledgments
The author thanks Professor V.N. Berestovskii for useful discussions and remarks.
Funding
The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0003).
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Translated from Sibirskii Matematicheskii Zhurnal, 2024, Vol. 65, No. 2, pp. 295–317. https://doi.org/10.33048/smzh.2024.65.206
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Zubareva, I.A. Geodesics and Shortest Arcs of Some Sub-Riemannian Metrics on the Lie Groups \( \operatorname{SU}(1,1)\times 𝕉 \) and \( \operatorname{SO}_{0}(2,1)\times 𝕉 \) with Three-Dimensional Generating Distributions. Sib Math J 65, 295–315 (2024). https://doi.org/10.1134/S003744662402006X
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DOI: https://doi.org/10.1134/S003744662402006X
Keywords
- geodesic
- left-invariant sub-Riemannian metric
- Lie algebra
- Lie group
- shortest arc
- cut locus
- first conjugate locus