orthonormal frame
{{Short description|Concept in Riemannian geometry}}
{{about-distinguish|local coordinates for manifolds|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 gP.{{citation|title=Introduction to Smooth Manifolds|volume=218|series=Graduate Texts in Mathematics|first=John|last=Lee|year=2013|edition=2nd|publisher=Springer|isbn= 9781441999825|page=178|url=https://books.google.com/books?id=xygVcKGPsNwC&pg=PA178}}.