Some Applications of Group Actions in Complex Geometry

GUAN Daniel

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

Chinese Quarterly Journal of Mathematics >

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

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

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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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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GUAN Daniel . Some Applications of Group Actions in Complex Geometry[J]. Chinese Quarterly Journal of Mathematics, 2023 , 38(3) : 254 -275 . DOI: 10.13371/j.cnki.chin.q.j.m.2023.03.002

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