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Open Riemannian manifold

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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.