Quasi-positively Ricci-curved Riemannian manifold

This article defines a property that makes sense for a Riemannian metric over a differential manifold

Definition

Symbol-free definition

A Riemannian manifold $M$ is said to have quasi-positive Ricci curvature if it satisfies the following two conditions:

• The Ricci curvature is everywhere nonnnegative
• There is a point on the manifold at which the Ricci curvature is strictly positive in all directions

Relation with other properties

Stronger properties

• Riemannian manifold with quasi-positive sectional curvature
• Positively Ricci-curved Riemannian manifold
• Positively curved Riemannian manifold