Orthonormal frame

This article is about local coordinates for manifolds and 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.^[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.