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 $\partial \bar{\partial }$-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 $h$-$\partial \bar{\partial }$-property is deformation open by constructing and studying a new notion called $hp$-Hermitian symplectic ($hp$-HS) form.

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