Quasi-positively curved Riemannian manifold

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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

Weaker properties