# Difference between revisions of "Riemannian manifold"

From Diffgeom

m (3 revisions) |
|||

(One intermediate revision by the same user not shown) | |||

Line 17: | Line 17: | ||

* [[Pseudo-Riemannian manifold]] | * [[Pseudo-Riemannian manifold]] | ||

+ | * [[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

## Contents

## Definition

A **Riemannian manifold** is the following data:

- A differential manifold
- A Riemannian metric on , viz a smooth association of a positive definite symmetric bilinear form for the tangent space .

## Relation with other structures

### Stronger structures

### Weaker structures

- Pseudo-Riemannian manifold
- Metric space
`Further information: Riemannian manifold is metric space`