Quasi-positively Ricci-curved Riemannian manifold

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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