2017/11/08 by Xiaokui Yang, Fangyang Zheng · 3 citations
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Algebraic Geometry and Number Theory #Curvature #Mathematics #Sectional curvature #Holomorphic function #Pure mathematics #Hermitian manifold #Hermitian matrix #Canonical bundle #Metric (unit) #Line bundle #Mathematical analysis #Topology (electrical circuits) #Scalar curvature #Geometry #Combinatorics
paper · pdf · doi:10.1090/tran/7445
openalex publication_date 2017/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/27
Motivated by the recent work of Wu and Yau on the ampleness of a canonical line bundle for projective manifolds with negative holomorphic sectional curvature, we introduce a new curvature notion called real bisectional curvature for Hermitian manifolds. When the metric is Kähler, this is just the holomorphic sectional curvature H, and when the metric is non-Kähler, it is slightly stronger than H. We classify compact Hermitian manifolds with constant nonzero real bisectional curvature, and also slightly extend Wu and Yauâs theorem to the Hermitian case. The underlying reason for the extension is that the Schwarz lemma of Wu and Yau works the same when the target metric is only Hermitian but has nonpositive real bisectional curvature.