Non-invariant deformations of left-invariant complex structures on compact Lie groups

被引：0

作者：

Ishida, Hiroaki ^{[1
]}

Kasuya, Hisashi ^{[2
]}

机构：

[1] Kagoshima Univ, Grad Sch Sci & Engn, Dept Math & Comp Sci, Kagoshima, Japan

[2] Osaka Univ, Grad Sch Sci, Dept Math, Osaka, Japan

来源：

FORUM MATHEMATICUM | 2022年 / 34卷 / 04期

关键词：

Compact Lie group; (non-)invariant complex structure; deformation; cohomology of holomorphic vector bundle; HOLOMORPHIC FLOWS; COHOMOLOGY;

D O I：

10.1515/forum-2021-0133

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give small deformations of a left-invariant complex structure on each simply connected semisimple compact Lie group of even dimension which are not biholomorphic to any left-invariant (right-invariant) complex structure by using the Kuranishi space. On such deformed complex manifolds, we prove the Borel-Weil-Bott type theorem, and we compute the cohomology of holomorphic tangent bundles.

引用

页码：907 / 918

页数：12

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