Comparison and vanishing theorems for Kähler manifolds

Abstract

In this paper, we consider orthogonal Ricci curvature $Ri{c}^{\perp }$ for Kähler manifolds, which is a curvature condition closely related to Ricci curvature and holomorphic sectional curvature. We prove comparison theorems and a vanishing theorem related to these curvature conditions, and construct various examples to illustrate their subtle relationship.

References in corpus (2)

• RC-positivity, rational connectedness and Yau's conjecture
• Gap theorem on Kähler manifold with nonnegative orthogonal bisectional curvature

Cited by in corpus (6)

• RC-positive metrics on rationally connected manifolds
• Estimation and Vanishing Results for Hodge numbers
• Manifolds with positive orthogonal Ricci curvature
• Quantitative comparison theorems in Riemannian and Kähler geometry
• Positive curvature operator, projective manifold and rational connectedness
• Deformation of Hermitian metrics