Constant-scalar curvature metric: Difference between revisions
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* [[Homogeneous metric]] | * [[Homogeneous metric]] | ||
* [[Locally homogeneous metric]] | * [[Locally homogeneous metric]] | ||
* [[Zero-scalar curvature metric]] | |||
===Weaker properties=== | ===Weaker properties=== | ||
* [[Constantly signed-scalar curvature metric]] | * [[Constantly signed-scalar curvature metric]] | ||
Revision as of 08:24, 25 April 2007
This article defines a property that makes sense for a Riemannian metric over a differential manifold
This is the property of the following curvature being constant: scalar curvature
Definition
Symbol-free definition
A Riemannian metric on a differential manifold is said to be a constant-scalar curvature metric if the scalar curvature at all points is equal.
Definition with symbols
Fill this in later
Relation with other properties
Stronger properties
The following properties of Riemannian metrics are stronger than the property of being a constant-scalar curvature metric:
- Constant-curvature metric
- Einstein metric
- Ricci-flat metric
- Homogeneous metric
- Locally homogeneous metric
- Zero-scalar curvature metric