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arXiv · 2306.02981

A note on compatibility of special Hermitian structures

Daniele Angella·Alexandra Otiman
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Abstract

We prove that a compact Vaisman manifold $(M, J)$ cannot admit some type of special Hermitian metrics, such as special $k$-Gauduchon metrics, $p$-K\"ahler forms, Hermitian-symplectic or strongly Gauduchon metrics compatible to the same complex structure $J$. In particular, it cannot admit pluriclosed or balanced metrics. We also investigate the interplay between locally conformally symplectic forms taming the complex structure $J$ and special Hermitian structures.

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Daniele Angella, Alexandra Otiman. 2023-06-05. A note on compatibility of special Hermitian structures. https://arxiv.org/abs/2306.02981

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