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.
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“We are not permitted to choose the frame of our destiny. But what we put into it is ours.”
—Dag Hammarskjöld (1905–1961)