Orthonormal frame

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 g_P.^[1]

See also

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

References

1. Lee, John (2013), Introduction to Smooth Manifolds, Graduate Texts in Mathematics, vol. 218 (2nd ed.), Springer, p. 178, ISBN 9781441999825.