Riemannian manifold

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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