Orthonormal frame

This article is about local coordinates for manifolds; it is not to be confused with Orthonormal frame (Euclidean geometry).

In Riemannian geometry and relativity theory, an orthonormal frame is a tool for studying the structure of a differentiable manifold equipped with a metric. If M is a manifold equipped with a metric g, then an orthonormal frame at a point P of M is an ordered basis of the tangent space at P consisting of vectors which are orthonormal with respect to the bilinear form g_P.

See also

• Frame (linear algebra)
• Frame bundle
• k-frame
• Moving frame
• Frame fields in general relativity