Parallel Translation on K\"{a}hler Manifolds

Citation:

Rongmu YAN.Parallel Translation on K\"{a}hler Manifolds[J].Chinese Annals of Mathematics B,2020,41(3):451~464
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Authors:

Rongmu YAN;

Foundation:

This work was supported by the National Natural Science Foundation of China (Nos.11571287, 11871405), the Fundamental Research Funds for the Central Universities (No.20720150006) and the Natural Science Foundation of Fujian Province of China (No.2016J01034).
Abstract: In this paper, the author establishs a real-valued function on K\"{a}hler manifolds by holomorphic sectional curvature under parallel translation. The author proves if such functions are equal for two simply-connected, complete K\"{a}hler manifolds, then they are holomorphically isometric.

Keywords:

K"{a}hler manifold, Holomorphic sectional curvature, Paralleltranslation

Classification:

32Q15
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