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Riemannian Geometry is a subfield of Differential Geometry, which specifically studies "Riemannian Manifolds", manifolds with "Riemannian Metrics", which means that they are equipped with continuous inner products.

4 votes

Testing for Riemannian isometry

Here's an irresponsible under-referenced response. On the one hand, this is hard! Indeed, I've read somewhere --- not handy --- that this question lurks among quantum gravity's many difficulties. Fo …
some guy on the street's user avatar
8 votes

When is a Riemannian manifold an open subset of a complete one?

If I understand you right, you're assuming that there is already a Riemann metric chosen for you. This of course integrates to a distance function ("metric" in the sense of metric spaces) whether or …
some guy on the street's user avatar