Riemannian manifold
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:
- 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