Homogeneous metric

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

Definition

Given data

A differential manifold $M$ equipped with a Riemannian metric $g$.

Definition part

The metric $g$ is said to be a homogeneous metric if given any points $x,y\in M$, there exists an isometry of $M$ sending $x$ to $y$.

Relation with other properties

Weaker properties

• Locally homogeneous metric
• Complete metric