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arXiv · 2309.09820

Killing fields on compact pseudo-Kähler manifolds

Andrzej Derdzinski·Ivo Terek
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Abstract

We show that a Killing field on a compact pseudo-Kähler 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-Kähler 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.

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Andrzej Derdzinski, Ivo Terek. 2024-01-16. Killing fields on compact pseudo-Kähler manifolds. https://doi.org/10.1007/s12220-024-01591-z

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