Vanishing theorems on compact Chern-K\"ahler-like Hermitian manifolds
Abstract
We show that, under the definiteness of holomorphic sectional curvature, the spaces of some holomorphic tensor fields on compact Chern-K\"ahler-like Hermitian manifolds are trivial. These can be viewed as counterparts to Bochner's classical vanishing theorems on compact K\"ahler manifolds under the definiteness of Ricci curvature or the existence of K\"ahler-Einstein metrics. Our proof is inspired by and based on some ideas due to X. Yang and L. Ni-F. Zheng.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.