Quasi-positively Ricci-curved Riemannian manifold: Difference between revisions
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===Symbol-free definition=== | ===Symbol-free definition=== | ||
A [[Riemannian manifold]] <math>M</math> is said to have '''quasi-positive Ricci curvature''' if it satisfies the following two conditions: | A [[Riemannian manifold]] <math>M</math> 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 | * The Ricci curvature is everywhere nonnnegative | ||
* There is a point on the manifold at which the Ricci curvature is strictly positive in all directions | * 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== | ==Relation with other properties== | ||
Revision as of 11:45, 7 July 2007
This article defines a property that makes sense for a Riemannian metric over a differential manifold
Definition
Symbol-free definition
A Riemannian manifold 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