Isotropic 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 said to be isotropic if given any two frames (ordered orthonormal bases) at a point, there is an isometry of the whole space taking one frame to the other.

Relation with other properties

A metric that is both homogeneous and isotropic is in fact a constant-curvature metric.