Riemannian manifold

It is a manifold together with a Riemannian metric. They can be generalized to pseudo-Riemannian manifolds.

They are, to a certain extent, a kind of metric space. The Hopf-Rinow theorem tells when they are metric spaces (indeed, Cauchy complete metric spaces).

They have a natural volume form.

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Author of the notes: Antonio J. Pan-Collantes

antonio.pan@uca.es