Riemannian manifold

From Diffgeom

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
  2. 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