Manifolds with positive orthogonal Ricci curvature

Abstract

In this paper we study the class of compact Kähler manifolds with positive orthogonal Ricci curvature: $Ri{c}^{\perp }>0$. First we illustrate examples of Kähler manifolds with $Ri{c}^{\perp }>0$ on Kähler C-spaces, and construct ones on certain projectivized vector bundles. These examples show the abundance of Kähler manifolds which admit metrics of $Ri{c}^{\perp }>0$. Secondly we prove some (algebraic) geometric consequences of the condition $Ri{c}^{\perp }>0$ to illustrate that the condition is also quite restrictive. Finally this last point is made evident with a classification result in dimension three and a partial classification in dimension four.

References in corpus (1)

• Comparison and vanishing theorems for Kähler manifolds

Cited by in corpus (3)

• Kähler manifolds and cross quadratic bisectional curvature
• Positive curvature operator, projective manifold and rational connectedness
• Diameter theorems on Kähler and quaternionic Kähler manifolds under a positive lower curvature bound