A note on compatibility of special Hermitian structures

Author:

Daniele Angella, Alexandra Otiman

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Complex Variables (math.CV)

journal:

date:

2023-06-04 16:00:00

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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