On local holomorphic maps between Hermitian manifolds preserving $(p,p)$-forms

TL;DR

This paper extends previous results on local holomorphic maps between Hermitian manifolds, focusing on those preserving -pb forms, leading to new rigidity and non-existence theorems.

Contribution

It generalizes existing results to broader classes of maps and establishes new rigidity and non-existence theorems for -pb form-preserving holomorphic maps.

Findings

Derived new rigidity theorems for -pb form-preserving maps.

Proved non-existence results under certain conditions.

Extended previous results to more general Hermitian manifolds.

Abstract

In this article, we generalize some results in Chan-Yuan [Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 26 (2025), 619--644] to local holomorphic maps between Hermitian manifolds preserving $(p,p)$-forms. In particular, we obtain further rigidity theorems and non-existence theorems for such maps.