Harmonic 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 termed a harmonic metric if the volume of any geodesic sphere is dependent only on its radius and is independent of the choice of center.

Relation with other properties

Stronger properties

• Homogeneous metric

Weaker properties

• Einstein metric