Editing 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]] ''g''<sub>''P''</sub>.<ref>{{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}}.</ref>

== See also ==
*[[Frame (linear algebra)]]
*[[Frame bundle]]
*[[k-frame|''k''-frame]]
*[[Moving frame]]
*[[Frame fields in general relativity]]

==References==
{{reflist}}

[[Category:Riemannian geometry]]


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