# Open Riemannian manifold

From Diffgeom

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

## Definition

A Riemannian manifold is said to be **open'** if it can be embedded as an open subset of Euclidean space in such a way that the Riemannian metric on the manifold is simply the restriction to the manifold of the usual metric on Euclidean space.