Difference between revisions of "Riemannian manifold"

From Diffgeom
Jump to: navigation, search
(Weaker structures)
Line 17: Line 17:
  
 
* [[Pseudo-Riemannian manifold]]
 
* [[Pseudo-Riemannian manifold]]
 +
* [[Metric space]] {{further|[[Riemannian manifold is metric space]]}}

Revision as of 10:58, 31 August 2007

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