Vanishing theorems and rational connectedness on holomorphic tensor fields
Abstract
A vanishing theorem for uniformly RC k k -positive Hermitian holomorphic vector bundles is established. It turns out that the holomorphic tangent bundle of a compact complex manifold equipped with a positive k k -Ricci curvature Kähler metric is uniformly RC k k -positive. Two main applications are presented. The first one is to deduce that spaces of some holomorphic tensor fields on such Kähler or more generally Kähler-like Hermitian manifolds are trivial, generalizing some recent results. The second one is to show that a compact Kähler manifold whose holomorphic tangent bundle can be endowed with either a uniformly RC k k -positive Hermitian metric or a positive k k -Ricci curvature Kähler-like Hermitian metric is projective and rationally connected.
Fields of Study & Subjects
Geometry and complex manifolds
Geometric Analysis and Curvature Flows
Advanced Differential Geometry Research
Publication details
- Journal / source
- Transactions of the American Mathematical Society
- Volume
- 379
- Issue
- 9
- Pages
- 6145–6165
- Publication date
- 18 March 2026
- Language
- EN