On Some Recent Progress in Complex Geometry-the Area Related to Homogeneous Manifolds  

关于复几何中的一些新进展--与齐性流形相关领域

作　　者：GUAN Daniel 关庄丹(School of Mathematics and Statistics,Henan University,Kaifeng 475004,China;Department of Mathematics,University of California at Riverside Riverside,CA 92521 U.S.A.)

机构地区：[1]School of Mathematics and Statistics,Henan University,Kaifeng 475004,China [2]Department of Mathematics,University of California at Riverside Riverside,CA 92521 U.S.A.

出　　处：《Chinese Quarterly Journal of Mathematics》2020年第2期111-144,共34页数学季刊（英文版）

基　　金：the Natural Science Foundation of Henan University。

摘　　要：In this article,we give a survey of some progress of the complex geometry,mostly related to the Lie group actions on compact complex manifolds and complex homogeneous spaces in the last thirty years.In particular,we explore some works in the special area in Di erential Geometry,Lie Group and Complex Homogeneous Space.Together with the special area in nonlinear analysis on complex manifolds,they are the two major aspects of my research interests.

关 键 词：Invariant structure Homogeneous space Complex torus bundles Hermitian manifolds Reductive Lie group Compact manifolds Ricci form Locally conformal Kahler manifolds 

分 类 号：O213.2[理学—概率论与数理统计]