2019/10/05 by Kai Tang, Tang, Kai
Mathematics · #53C24 #53C55 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1910.02363
openalex publication_date 2019/10/05 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
In this paper, we derive some \∂\\∂-Bochner formulas\nfor holomorphic maps between Hermitian manifolds. As applications, we prove\nsome Schwarz lemma type estimates, rigidity and degeneracy theorems. For\ninstance, we show that there is no non-constant holomorphic map from a comapct\nHermitian manifold with positive (resp. non-negative) \ℓ-second Ricci\ncurvature to a Hermitian manifold with non-positive (resp. negative) real\nbisectional curvature. These theorems generalize the results citeNi1,Ni2\nproved recently by L. Ni on K "ahler manifolds to Hermitian manifolds. We\nalso derive an integral inequality for holomorphic map between Hermitian\nmanifolds.\n