Glossary of Riemannian and metric geometry

This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology. The following articles may also be useful. These either contain specialised vocabulary or provide more detailed expositions of the definitions given below.

Related Topics:
Riemannian geometry - Metric geometry - Differential topology

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• Connection
• Curvature
• Metric space
• Riemannian manifold

See also:

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• Glossary of general topology
• Glossary of differential geometry and topology
• List of differential geometry topics

Unless stated otherwise, letters X, Y, Z below denote metric spaces, M, N denote Riemannian manifolds, |xy| or |xy|_X denotes the distance between points x and y in X. Italic word denotes a self-reference to this glossary.

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A caveat: many terms in Riemannian and metric geometry, such as convex function, convex set and others, do not have exactly the same meaning as in general mathematical usage.

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