Conformally flat metric

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

• Flat metric

Weaker properties

• Constant-scalar curvature metric