Curvature-transitive 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 curvature-transitive if given any two points with the same sectional curvature, there is an isometry of the manifold taking one to the other.

In other words, the sectional curvature is a complete invariant of the isometry class of a point.

Relation with other properties

Stronger properties

• Homogeneous metric