Difference between revisions of "Conformally flat metric"

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===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]].
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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]].
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==Relation with other properties==
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===Stronger properties==
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* [[Flat metric]]
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===Weaker properties===
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* [[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.

Relation with other properties

=Stronger properties

Weaker properties