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.

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

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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