THE ∂∂^(-)-BOCHNER FORMULAS FOR HOLOMORPHIC MAPPINGS BETWEEN HERMITIAN MANIFOLDS AND THEIR APPLICATIONS  

作　　者：Kai TANG 汤凯(College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua 321004,China)

机构地区：[1]College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua 321004,China

出　　处：《Acta Mathematica Scientia》2021年第5期1659-1669,共11页数学物理学报（B辑英文版）

基　　金：supported by National Natural Science Foundation of China(12001490);Natural Science Foundation of Zhejiang Province(LQ20A010005).

摘　　要：In this paper,we derive some∂∂^(-)-Bochner formulas for holomorphic maps between Hermitian manifolds.As applications,we prove some Schwarz lemma type estimates,and some rigidity and degeneracy theorems.For instance,we show that there is no non-constant holomorphic map from a compact Hermitian manifold with positive(resp.non-negative)ℓ-second Ricci curvature to a Hermitian manifold with non-positive(resp.negative)real bisectional curvature.These theorems generalize the results[5,6]proved recently by L.Ni on Kähler manifolds to Hermitian manifolds.We also derive an integral inequality for a holomorphic map between Hermitian manifolds.

关 键 词：Schwarz lemmas Bochner formulas holomorphic map Hermitian manifolds ℓ-second Ricci curvature 

分 类 号：O186.1[理学—数学]