Orthonormal frame
Concept in Riemannian geometry / From Wikipedia, the free encyclopedia
This article is about local coordinates for manifolds. For the use in Euclidean geometry, see Cartesian coordinates and Affine space § Affine coordinates.
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 gP.[1]