群作用在复几何中的一些运用

关庄丹

doi:10.13371/j.cnki.chin.q.j.m.2023.03.002

数学季刊 >

2023 , Vol. 38 >Issue 3: 254 - 275

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2023.03.002

群作用在复几何中的一些运用

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1. School of Mathematics and Statistics, Henan University, Kaifeng 475004, China; 2. Department of Mathematics, University of California at Riverside, CA 92521, U.S.A.

GUAN Daniel (1962-), male, native of Fuzhou, Fujian, professor of Henan University, engages in complex differential geometry.

收稿日期: 2023-09-03

网络出版日期: 2023-09-30

基金资助

This research is partially supported by NSFC (Grant No. 12171140).

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Some Applications of Group Actions in Complex Geometry

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1. School of Mathematics and Statistics, Henan University, Kaifeng 475004, China; 2. Department of Mathematics, University of California at Riverside, CA 92521, U.S.A.

GUAN Daniel (1962-), male, native of Fuzhou, Fujian, professor of Henan University, engages in complex differential geometry.

Received date: 2023-09-03

Online published: 2023-09-30

Supported by

This research is partially supported by NSFC (Grant No. 12171140).

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摘要

In this article, we give a further survey of some progress of the applications of group actions in the complex geometry after my earlier survey around 2020, mostly related to my own interests.

关键词： Invariant structure; Homogeneous space; Fiber bundles; Hermitian manifolds; Reductive Lie group; Compact manifolds; Chern class; Co-homogeneity one K¨ahler manifolds

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关庄丹 . 群作用在复几何中的一些运用[J]. 数学季刊, 2023 , 38(3) : 254 -275 . DOI: 10.13371/j.cnki.chin.q.j.m.2023.03.002

Abstract

In this article, we give a further survey of some progress of the applications of group actions in the complex geometry after my earlier survey around 2020, mostly related to my own interests.

Key words： Invariant structure; Homogeneous space; Fiber bundles; Hermitian manifolds; Reductive Lie group; Compact manifolds; Chern class; Co-homogeneity one K¨ahler manifolds

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