# Curvature-transitive metric

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

## Contents

## 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.