On local stabilities of $p$-Kähler structures

Abstract

By use of a natural extension map and a power series method, we obtain a local stability theorem for p-Kähler structures with the $(p,p+1)$-th mild $\partial \bar{\partial }$-lemma under small differentiable deformations.

Several typos have been fixed. Final version to appear in Compositio Mathematica. arXiv admin note: text overlap with arXiv:1609.05637

References in corpus (6)

• Lie-algebra Dolbeault cohomology and small deformations of nilmanifolds
• On small deformations of balanced manifolds
• Locally conformal Hermitian metrics on complex non-Kähler manifolds
• Extension formulas and deformation invariance of Hodge numbers
• Quantitative and qualitative cohomological properties for non-Kähler manifolds
• Hodge theory for twisted differentials

Cited by in corpus (4)

• Deformations of Dolbeault cohomology classes
• Deformations of Dolbeault cohomology classes for Lie algebra with complex structures
• A note on $p$-Kähler structures on compact quotients of Lie groups
• On extension of closed complex (basic) differential forms: (basic) Hodge numbers and (transversely) $p$-Kähler structures