Vanishing theorems on compact Chern-Kähler-like Hermitian manifolds

Abstract

We show that, under the definiteness of holomorphic sectional curvature, the spaces of some holomorphic tensor fields on compact Chern-Kähler-like Hermitian manifolds are trivial. These can be viewed as counterparts to Bochner's classical vanishing theorems on compact Kähler manifolds under the definiteness of Ricci curvature or the existence of Kähler-Einstein metrics. Our proof is inspired by and based on some ideas due to X. Yang and L. Ni-F. Zheng.

10 pages, accepted by Mathematical Research Letters

Cited by in corpus (1)

• Vanishing theorems and rational connectedness on holomorphic tensor fields