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A note on compatibility of special Hermitian structures

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arxiv 2306.02981 v2 pith:4XGHOXQB submitted 2023-06-05 math.DG math.CV

Daniele Angella , Alexandra Otiman This is my paper · ORCID
classification math.DGmath.CV
keywords metricsspecialhermitianadmitcannotcomplexformsgauduchon
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Fino--Vezzoni conjecture on homogeneous spaces

    math.DG 2026-08 conditional novelty 8.0 of 10

    Compact quotients of complex homogeneous spaces with compact isotropy are Kähler whenever they admit both a balanced metric and a pluriclosed metric.

  2. Special non-K\"ahler metrics -- old and new

    math.DG 2025-05 unverdicted

    An expository account of non-Kähler metric classes, their incompatibilities, and their stability, with all results cited from previous papers.

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