Killing fields on compact pseudo-Kähler manifolds

We show that a Killing field on a compact pseudo-K\"ahler ddbar manifold is necessarily (real) holomorphic. Our argument works without the ddbar assumption in real dimension four. The claim about holomorphicity of Killing fields on compact pseudo-K\"ahler manifolds appears in a 2012 paper...

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Bibliographic Details
Published in:arXiv.org 2024-01
Main Authors: Derdzinski, Andrzej, Terek, Ivo
Format: Article
Language:English
Subjects:
Mathematical analysis
Online Access:Get full text
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Summary:We show that a Killing field on a compact pseudo-K\"ahler ddbar manifold is necessarily (real) holomorphic. Our argument works without the ddbar assumption in real dimension four. The claim about holomorphicity of Killing fields on compact pseudo-K\"ahler manifolds appears in a 2012 paper by Yamada, and in an appendix we provide a detailed explanation of why we believe that Yamada's argument is incomplete.
ISSN:2331-8422
DOI:10.48550/arxiv.2309.09820