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

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.

To appear in Proceedings of the American Mathematical Society; V2: Corrections of typos and minor errors in the proof of Lemma 4.3; V3: Minor changes in the proof of Theorem 4.1