Extension formulae on almost complex manifolds

TL;DR

This paper develops extension formulae for almost complex manifolds, providing decompositions and applications to forms and cohomology, advancing understanding of complex structures in differential geometry.

Contribution

It introduces new extension formulae and decompositions on almost complex manifolds, with applications to forms and cohomology groups.

Findings

Derived extension formulae for almost complex manifolds

Decompositions of the extension formulae

Applications to $(n,0)$-forms and Dolbeault cohomology

Abstract

We give the extension formulae on almost complex manifolds and give decompositions of the extension formulae. As applications, we study $(n,0)$-forms, the $(n,0)$-Dolbeault cohomology group and $(n,q)$-forms on almost complex manifolds.