Constant-scalar curvature metric: Difference between revisions
| Line 19: | Line 19: | ||
The following properties of Riemannian metrics are stronger than the property of being a constant-scalar curvature metric: | The following properties of Riemannian metrics are stronger than the property of being a constant-scalar curvature metric: | ||
* [[Flat metric]] | |||
* [[Conformally flat metric]] | |||
* [[Constant-curvature metric]] | * [[Constant-curvature metric]] | ||
* [[Einstein metric]] | * [[Einstein metric]] | ||
Revision as of 09:41, 2 September 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:
- Flat metric
- Conformally flat metric
- Constant-curvature metric
- Einstein metric
- Ricci-flat metric
- Homogeneous metric
- Locally homogeneous metric
- Zero-scalar curvature metric