# Riemannian manifold

*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`