A note on compatibility of special Hermitian structures

2023/06/05 by Angella, Daniele, Otiman, Alexandra · 2 citations
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.02981

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-Kähler 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.

Cited by

• Constant holomorphic sectional curvature conjecture and Fino-Vezzoni conjecture
• Calabi-Yau locally conformally Kähler manifolds

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• Compatibility between non-Kähler structures on complex (nil)manifolds
• Special Hermitian metrics
• Streets-Tian Conjecture on several special types of Hermitian manifolds
• Balanced metrics and Gauduchon cone of locally conformally Kahler manifolds
• An integral condition involving ∂-harmonic (0,1)-forms