# Isotropic metric

From Diffgeom

*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 **isotropic** if given any two frames (ordered orthonormal bases) at a point, there is an isometry of the whole space taking one frame to the other.

## Relation with other properties

A metric that is both homogeneous and isotropic is in fact a constant-curvature metric.