On mixed curvature for Hermitian manifolds
Abstract
We consider mixed curvature C α,β for Hermitian manifolds, which is a convex combination of the first Chern Ricci curvature and holomorphic sectional curvature introduced by Chu, Lee and Tam (2022).We prove that if a compact Hermitian surface has constant mixed curvature c, then the Hermitian metric must be Kähler unless c = 0 and 2α +β = 0, which extends a previous result by Apostolov, Davidov and Mushkarov (1996).For the higher-dimensional case, we also partially classify compact locally conformal Kähler manifolds with constant mixed curvature.Lastly, we prove that if β ≥ 0 and α(n+1)+2β > 0, then a compact Hermitian manifold with semipositive but not identically zero mixed curvature has Kodaira dimension -∞.
Fields of Study & Subjects
Geometry and complex manifolds
Geometric Analysis and Curvature Flows
Geometric and Algebraic Topology
Publication details
- Journal / source
- Pacific Journal of Mathematics
- Volume
- 344
- Issue
- 1
- Pages
- 201–218
- Publication date
- 10 August 2026
- Language
- EN