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

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 <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis p comma p right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>p</mml:mi> <mml:mo>,</mml:mo> <mml:mi>p</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">(p,p)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -forms. In particular, we obtain further rigidity theorems and non-existence theorems for such maps.