Chinese Quarterly Journal of Mathematics ›› 2020, Vol. 35 ›› Issue (2): 111-144.doi: 10.13371/j.cnki.chin.q.j.m.2020.02.001

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

  

  1. 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.
  • Received:2019-12-15 Online:2020-06-30 Published:2020-08-23
  • Contact: GUAN Daniel (1962-), Male, native of Fuzhou, Fujian, a professor of Henan University, engages in complex di erential geometry.
  • About author:GUAN Daniel (1962-), Male, native of Fuzhou, Fujian, a professor of Henan University, engages in complex di erential geometry.
  • Supported by:
    Supported by the Natural Science Foundation of Henan University

Abstract: 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.

Key words: Invariant structure, Homogeneous space, Complex torus bundles, Hermitian manifolds, Reductive Lie group, Compact manifolds, Ricci form, Locally conformal Kahler manifolds

CLC Number: