Quasi-positively curved Riemannian manifold

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

This article defines a property of Riemannian metrics based on the behaviour of the following curvature: sectional curvature

Definition

A Riemannian manifold $M$ is said to have quasi-positive sectional curvature or to be quasi-positively curved if the following are true:

• The sectional curvature is everywhere nonnegative
• There is a point for which the sectional curvature is strictly positive for all tangent planes

Relation with other properties

Stronger properties

• Positively curved Riemannian manifold

Weaker properties

• Nonnegatively curved Riemannian manifold
• Quasi-positive Ricci-curved Riemannian manifold