Curvature-transitive metric

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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