# Conformally flat metric

From Diffgeom

*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.