Locally homogeneous metric
From Diffgeom
This article defines a property that makes sense for a Riemannian metric over a differential manifold
Contents
Definition
Given data
A differential manifold equipped with a Riemannian metric
.
Definition part
is said to be locally homogeneous if for any
we can find neighbourhoods
and
of those and a Riemannian isometry between
and
that takes
to
.
Relation with other properties
Stronger properties
- Constant-curvature metric
- Homogeneous metric: The two properties become equivalent when the manifold is simply connected