On local stabilities of $p$-K\"ahler structures

TL;DR

This paper proves a local stability theorem for p-K"ahler structures under small deformations, utilizing a natural extension map and power series method, especially when the $(p,p+1)$-th mild $ar{ ext{d}}ar{ ext{d}}$-lemma holds.

Contribution

It introduces a new stability theorem for p-K"ahler structures using a novel approach with extension maps and power series, expanding understanding of their deformation behavior.

Findings

Established local stability of p-K"ahler structures

Applied the theorem to structures satisfying the $(p,p+1)$-th mild $ar{ ext{d}}ar{ ext{d}}$-lemma

Extended the deformation theory of complex structures

Abstract

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