Killing fields on compact pseudo-K\"ahler manifolds
Differential Geometry
2024-12-19 v3
Abstract
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.
Keywords
Cite
@article{arxiv.2309.09820,
title = {Killing fields on compact pseudo-K\"ahler manifolds},
author = {Andrzej Derdzinski and Ivo Terek},
journal= {arXiv preprint arXiv:2309.09820},
year = {2024}
}
Comments
Small parts text rearranged; some clarifying sentences added; a few typos corrected