Orthonormal frame

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.

This article is about local coordinates for manifolds. For the use in Euclidean geometry, see Cartesian coordinates and Affine space ยง Affine coordinates.
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