Inspired by the work of Lu and Tian (Duke Math J 125:351--387, 2004), Loi et al. address in (Abh Math Semin Univ Hambg 90: 99-109, 2020) the problem of studying those Kähler manifolds satisfying the \(\Delta \)-property, i.e. such that on a neighborhood of each of its points the k-th power of the Kähler Laplacian is a polynomial function of the complex Euclidean Laplacian, for all positive integer k. In particular they conjectured that if a Kähler manifold satisfies the \(\Delta \)-property then it is a complex space form. This paper is dedicated to the proof of the validity of this conjecture.

Loi等人的灵感来自Lu和Tian（Duke Math J 125：351--387，2004）。（Abh Math Semin Univ Hambg 90：99-109，2020）中解决的问题是研究满足\（\ Delta \）性质的那些Kähler流形，即使得在其每个点的邻域中第k次幂对于所有正整数k，KählerLaplacian的多项式是复数Euclidean Laplacian的多项式函数。特别是他们推测，如果Kähler流形满足\（\ Delta \） -属性，则它是一个复杂的空间形式。本文致力于证明这一猜想的有效性。