Locally homogeneous metric

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

Definition

Given data

A differential manifold M equipped with a Riemannian metric g.

Definition part

g is said to be locally homogeneous if for any x,y \in M we can find neighbourhoods U_x and U_y of those and a Riemannian isometry between U_x and U_y that takes x to y.

Relation with other properties

Stronger properties

Weaker properties