Riemannian manifold

From Diffgeom
Revision as of 20:07, 18 May 2008 by Vipul (talk | contribs) (3 revisions)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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 M
  2. A Riemannian metric g on M, viz a smooth association of a positive definite symmetric bilinear form g_p for the tangent space T_p(M).

Relation with other structures

Stronger structures

Weaker structures