局部共形拟 Kähler Finsler 流形

doi:10.13371/j.cnki.chin.q.j.m.2021.03.003

数学季刊 ›› 2021, Vol. 36 ›› Issue (3): 244-251.doi: 10.13371/j.cnki.chin.q.j.m.2021.03.003

局部共形拟 Kähler Finsler 流形

School of Mathematics and Statistics, Henan University

收稿日期:2021-06-09 出版日期:2021-09-30 发布日期:2021-10-08
作者简介: LI Hong-jun (1986-), male, native of Fugou, Henan, lecturer of Henan University, engages in function theory of several complex variables.
基金资助:
Supported by the National Natural Science Foundation of China (Grant No. 12001165);

Postdoctoral Research Foundation of China (Grant No. 2019M652513);

Postdoctoral Research Foundation of Henan Province (Grant No. 19030050).

Locally Conformal Pseudo-Kähler Finsler Manifolds

School of Mathematics and Statistics, Henan University

Received:2021-06-09 Online:2021-09-30 Published:2021-10-08
About author: LI Hong-jun (1986-), male, native of Fugou, Henan, lecturer of Henan University, engages in function theory of several complex variables.
Supported by:
Supported by the National Natural Science Foundation of China (Grant No. 12001165);

Postdoctoral Research Foundation of China (Grant No. 2019M652513);

Postdoctoral Research Foundation of Henan Province (Grant No. 19030050).

摘要/Abstract

摘要： In this paper, we give a necessary and sufficient condition for a strongly pseudoconvex complex Finsler metric to be locally conformal pseudo-Kähler Finsler. As an application, we find any complete strongly convex and locally conformal pseudo-Kähler Finsler manifold, which is simply connected or whose fundamental group contains elements of finite order only, can be given a Kähler metric.

关键词: Strongly pseudoconvex complex Finsler metric, Locally conformal pesudo-K?hler Finsler metric, K?hler metric

Abstract: In this paper, we give a necessary and sufficient condition for a strongly pseudoconvex complex Finsler metric to be locally conformal pseudo-Kähler Finsler. As an application, we find any complete strongly convex and locally conformal pseudo-Kähler Finsler manifold, which is simply connected or whose fundamental group contains elements of finite order only, can be given a Kähler metric.

Key words: Strongly pseudoconvex complex Finsler metric, Locally conformal pesudo-K?hler Finsler metric, K?hler metric

中图分类号:

O174.56

李鸿军. 局部共形拟 Kähler Finsler 流形[J]. 数学季刊, 2021, 36(3): 244-251.

LI Hong-jun. Locally Conformal Pseudo-Kähler Finsler Manifolds[J]. Chinese Quarterly Journal of Mathematics, 2021, 36(3): 244-251.

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局部共形拟 Kähler Finsler 流形

Locally Conformal Pseudo-Kähler Finsler Manifolds

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