Quasi-positively curved Riemannian manifold: Difference between revisions
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==Definition== | ==Definition== | ||
A [[Riemannian manifold]] <math>M</math> is said to have '''quasi-positive sectional curvature''' if the following are true: | A [[Riemannian manifold]] <math>M</math> 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 | * The sectional curvature is everywhere nonnegative | ||
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* [[Nonnegatively curved Riemannian manifold]] | * [[Nonnegatively curved Riemannian manifold]] | ||
* [[ | * [[Quasi-positive Ricci-curved Riemannian manifold]] | ||
Latest revision as of 19:51, 18 May 2008
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 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