A note on compatibility of special Hermitian structures
Differential Geometry
2023-06-08 v2 Complex Variables
Abstract
We prove that a compact Vaisman manifold cannot admit some type of special Hermitian metrics, such as special -Gauduchon metrics, -K\"ahler forms, Hermitian-symplectic or strongly Gauduchon metrics compatible to the same complex structure . In particular, it cannot admit pluriclosed or balanced metrics. We also investigate the interplay between locally conformally symplectic forms taming the complex structure and special Hermitian structures.
Cite
@article{arxiv.2306.02981,
title = {A note on compatibility of special Hermitian structures},
author = {Daniele Angella and Alexandra Otiman},
journal= {arXiv preprint arXiv:2306.02981},
year = {2023}
}
Comments
(thanks to Adrian Andrada and Alejandro Tolcachier for pointing out a mistake in the previous version)