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- W3037421503 abstract "Inspired by the work of Lu and Tian (Duke Math J 125(2):351–387, 2004), in this paper we address the problem of studying those Kahler manifolds satisfying the $$Delta$$-property, i.e. such that on a neighborhood of each of its points the kth power of the Kahler Laplacian is a polynomial function of the complex Euclidean Laplacian, for all positive integer k (see below for its definition). We prove two results: (1) if a Kahler manifold satisfies the $$Delta$$-property then its curvature tensor is parallel; (2) if an Hermitian symmetric space of classical type satisfies the $$Delta$$-property then it is a complex space form (namely it has constant holomorphic sectional curvature). In view of these results we believe that if a Kahler manifold satisfies the $$Delta$$-property then it is a complex space form." @default.
- W3037421503 created "2020-07-02" @default.
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- W3037421503 date "2020-04-01" @default.
- W3037421503 modified "2023-10-08" @default.
- W3037421503 title "A characterization of complex space forms via Laplace operators" @default.
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- W3037421503 doi "https://doi.org/10.1007/s12188-020-00220-0" @default.
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