Difference between revisions of "Riemannian manifold"

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* [[Pseudo-Riemannian manifold]]
 
* [[Pseudo-Riemannian manifold]]
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* [[Metric space]] {{further|[[Riemannian manifold is metric space]]}}

Latest revision as of 20:07, 18 May 2008

This article defines a differential manifold with the following additional structure -- the structure group is reduced to: orthogonal group

Definition

A Riemannian manifold is the following data:

  1. A differential manifold M
  2. A Riemannian metric g on M, viz a smooth association of a positive definite symmetric bilinear form g_p for the tangent space T_p(M).

Relation with other structures

Stronger structures

Weaker structures