Oriented Orthonormal

Some articles on orthonormal, oriented, oriented orthonormal:

Orthonormal Frame Bundle
... 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 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 ...