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; they either contain specialised vocabulary or provide more detailed expositions of the definitions given below.

See also:

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

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.

A

Alexandrov space a generalization of Riemannian manifolds with upper, lower or integral curvature bounds (the last one works only in dimension 2)