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 ) (p,p) -forms. In particular, we obtain further rigidity theorems and non-existence theorems for such maps.
Shan Tai Chan (Fri,) studied this question.