Riemannian manifold
From Diffgeom
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