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群作用在复几何中的一些运用

Some Applications of Group Actions in Complex Geometry

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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.

作者 GUAN Daniel

机构地区 School of Mathematics and Statistics Department of Mathematics

出处《Chinese Quarterly Journal of Mathematics》 2023年第3期254-275,共22页 数学季刊（英文版）

基金 partially supported by NSFC(Grant No.12171140)。

关键词 Invariant structure Homogeneous space Fiber bundles Hermitian manifolds Reductive Lie group Compact manifolds Chern class Co-homogeneity one Kahler manifolds

分类号 O186.16 [理学—基础数学] O174.56 [理学—基础数学]

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参考文献4

1陈兵龙,朱熹平.YAU'S UNIFORMIZATION CONJECTURE FOR MANIFOLDS WITH NON-MAXIMAL VOLUME GROWTH[J].Acta Mathematica Scientia,2018,38(5):1468-1484. 被引量：3
2关庄丹.关于复几何中的一些新进展--与齐性流形相关领域[J].Chinese Quarterly Journal of Mathematics,2020,35(2):111-144. 被引量：1
3关庄丹.MAXWELL-EINSTEIN METRICS ON COMPLETIONS OF CERTAIN C* BUNDLES[J].Acta Mathematica Scientia,2023,43(1):363-372. 被引量：2
4唐梓洲,彦文娇.ISOPARAMETRIC HYPERSURFACES AND COMPLEX STRUCTURES[J].Acta Mathematica Scientia,2022,42(6):2223-2229. 被引量：1

二级参考文献2

1Chia Kuei PENG,Zi Zhou TANG(Zizhou TANG).Integrability Condition on an Almost Complex Structure and Its Application[J].Acta Mathematica Sinica,English Series,2005,21(6):1459-1464. 被引量：2
2陈兵龙,朱熹平.YAU'S UNIFORMIZATION CONJECTURE FOR MANIFOLDS WITH NON-MAXIMAL VOLUME GROWTH[J].Acta Mathematica Scientia,2018,38(5):1468-1484. 被引量：3

共引文献2

1关庄丹.关于复几何中的一些新进展--与齐性流形相关领域[J].Chinese Quarterly Journal of Mathematics,2020,35(2):111-144. 被引量：1
2段晓曼,关庄丹.COMPLETE KAHLER METRICS WITH POSITIVE HOLOMORPHIC SECTIONAL CURVATURES ON CERTAIN LINE BUNDLES(RELATED TO A COHOMOGENEITY ONE POINT OF VIEW ON A YAU CONJECTURE)[J].Acta Mathematica Scientia,2024,44(1):78-102.

1Rongmu YAN.Parallel Translation on Kahler Manifolds[J].Chinese Annals of Mathematics,Series B,2020,41(3):451-464.
2Jian Xiao.Mixed Hodge-Riemann bilinear relations and m-positivity[J].Science China Mathematics,2021,64(7):1703-1714.
3Ruixin WANG,Wen WANG,Songting YIN.Some Remarks on Higgs Bundles over Compact Generalized Kahler Manifolds[J].Journal of Mathematical Research with Applications,2021,41(5):537-550.
4本刊英文版2022年65卷第5期(887–1108)摘要(英文)[J].中国科学：数学,2022,52(5).
5本刊英文版2023年66卷第6期(1141-1394)摘要[J].中国科学：数学,2023,53(6).
6陶祥兴,曾媛,喻晓.BOUNDEDNESS AND COMPACTNESS FOR THE COMMUTATOR OF THEω-TYPE CALDER′ON-ZYGMUND OPERATOR ON LORENTZ SPACE[J].Acta Mathematica Scientia,2023,43(4):1587-1602.
7Yuxin DONG,Weike YU.Generalized Maximum Principles and Stochastic Completeness for Pseudo-Hermitian Manifolds[J].Chinese Annals of Mathematics,Series B,2022,43(6):949-976.
8Pei Pei RAO,Fang Yang ZHENG.Pluriclosed Manifolds with Constant Holomorphic Sectional Curvature[J].Acta Mathematica Sinica,English Series,2022,38(6):1094-1104.
9唐梓洲,彦文娇.ISOPARAMETRIC HYPERSURFACES AND COMPLEX STRUCTURES[J].Acta Mathematica Scientia,2022,42(6):2223-2229. 被引量：1
10Akito Futaki,Yingying Zhang.Coupled Sasaki-Ricci solitons[J].Science China Mathematics,2021,64(7):1447-1462.

Chinese Quarterly Journal of Mathematics

2023年第3期

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