Conformally flat metric: Difference between revisions
No edit summary |
No edit summary |
||
| Line 5: | Line 5: | ||
===Symbol-free definition=== | ===Symbol-free definition=== | ||
A [[Riemannian metric]] on a [[differential manifold]] is said to be '''conformally flat''' if every point has a neighbourhood such that the restriction to that neighbourhood, is conformally equivalent to the [[flat metric]]. | A [[Riemannian metric]] on a [[differential manifold]] is said to be '''conformally flat''' or '''locally conformally flat''' if every point has a neighbourhood such that the restriction to that neighbourhood, is conformally equivalent to the [[flat metric]]. | ||
==Relation with other properties== | |||
===Stronger properties== | |||
* [[Flat metric]] | |||
===Weaker properties=== | |||
* [[Constant-scalar curvature metric]] | |||
Revision as of 09:38, 2 September 2007
This article defines a property that makes sense for a Riemannian metric over a differential manifold
Definition
Symbol-free definition
A Riemannian metric on a differential manifold is said to be conformally flat or locally conformally flat if every point has a neighbourhood such that the restriction to that neighbourhood, is conformally equivalent to the flat metric.