Co-polarised Deformations of Gauduchon Calabi-Yau $\partial\bar{\partial}$-Manifolds and Deformation of $p$-SKT $h$-$\partial\bar{\partial}$-Manifolds

Abstract

The main result of this paper is to study the local deformations of Calabi-Yau ∂ ∂-manifold that are co-polarised by the Gauduchon metric by considering the subfamily of co-polarised fibres by the class of Aeppli/De Rham-Gauduchon cohomology of Gauduchon metric given at the beginning on the central fibre. In the latter part, we prove that the p-SKT h-∂ ∂-property is deformation open by constructing and studying a new notion called hp-Hermitian symplectic (hp-HS) form.