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 or to be quasi-positively Ricci-curved 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

References

• On the structure of complete manifolds on nonnegative Ricci curvature by Jeff Cheeger and Detlef Gromoll

Relation with other properties

Stronger properties

• Quasi-positively curved Riemannian manifold
• Positively Ricci-curved Riemannian manifold
• Positively curved Riemannian manifold