Locally conformal Hermitian metrics on complex non-Kähler manifolds

Abstract

We study complex non-Kähler manifolds with Hermitian metrics being locally conformal to metrics with special cohomological properties. In particular, we provide examples where the existence of locally conformal holomorphic-tamed structures implies the existence of locally conformal Kähler metrics, too.

References in corpus (2)

• On locally conformal symplectic manifolds of the first kind
• Hodge theory for twisted differentials

Cited by in corpus (7)

• On small deformations of balanced manifolds
• On local stabilities of $p$-Kähler structures
• Deformations of Dolbeault cohomology classes
• Cohomologies of locally conformally symplectic manifolds and solvmanifolds
• Almost formality of quasi-Sasakian and Vaisman manifolds with applications to nilmanifolds
• On extension of closed complex (basic) differential forms: (basic) Hodge numbers and (transversely) $p$-Kähler structures
• The hard Lefschetz duality for locally conformally almost Kähler manifolds