Locally Conformal Pseudo-Kähler Finsler Manifolds

LI Hong-jun

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

Chinese Quarterly Journal of Mathematics >

2021 , Vol. 36 >Issue 3: 244 - 251

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2021.03.003

Locally Conformal Pseudo-Kähler Finsler Manifolds

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School of Mathematics and Statistics, Henan University

LI Hong-jun (1986-), male, native of Fugou, Henan, lecturer of Henan University, engages in function theory of several complex variables.

Received date: 2021-06-09

Online published: 2021-10-08

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).

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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

Cite this article

LI Hong-jun . Locally Conformal Pseudo-Kähler Finsler Manifolds[J]. Chinese Quarterly Journal of Mathematics, 2021 , 36(3) : 244 -251 . DOI: 10.13371/j.cnki.chin.q.j.m.2021.03.003

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