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Licensed Unlicensed Requires Authentication Published by De Gruyter April 27, 2022

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

  • Hiroaki Ishida and Hisashi Kasuya EMAIL logo
From the journal Forum Mathematicum


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.

MSC 2010: 22E46; 32M05; 32M10; 32G05; 58A30; 32L10

Award Identifier / Grant number: JP20K03592

Award Identifier / Grant number: JP19H01787

Award Identifier / Grant number: JP21K03248

Funding statement: The first author is supported by JSPS KAKENHI Grant Number JP20K03592. The second author is supported by JSPS KAKENHI Grant Numbers JP19H01787, JP21K03248.


We are grateful to the anonymous referee for the invaluable comments and useful suggestions on improving the text.

  1. Communicated by: Shigeharu Takayama


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Received: 2021-05-30
Revised: 2022-04-01
Published Online: 2022-04-27
Published in Print: 2022-07-01

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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