# 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]]. | + | 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]] |

## Latest revision as of 19:34, 18 May 2008

*This article defines a property that makes sense for a Riemannian metric over a differential manifold*

## Contents

## 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.