### Some articles on *orthonormal, oriented, oriented orthonormal*:

Orthonormal Frame Bundle

... possible to talk about the set of all of

... possible to talk about the set of all of

**orthonormal**frames for Ex ... An**orthonormal**frame for Ex is an ordered**orthonormal**basis for Ex, or, equivalently, a linear isometry where Rk is equipped with the standard Euclidean metric ... group O(k) acts freely and transitively on the set of all**orthonormal**frames via right composition ...Riemannian Connection On A Surface - Orthonormal Frame Bundle

... An ordered basis or frame v, w in the tangent space is said to be

... An ordered basis or frame v, w in the tangent space is said to be

**oriented**if det(v, w) is positive ... The frame bundle E of M consists of triples (p, e1, e2) with an e1, e2 an**oriented orthonormal**basis of the tangent plane at p ... Since the group of rotations in the plane SO(2) acts simply transitively on**oriented orthonormal**frames in the plane, it follows that it also acts on the frame or circle bundles of M ...Main Site Subjects

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