Moving Frame - Moving Tangent Frames

Moving Tangent Frames

The most commonly encountered case of a moving frame is for the bundle of tangent frames (also called the frame bundle) of a manifold. In this case, a moving tangent frame on a manifold M consists of a collection of vector fields X₁, X₂, ..., X_n forming a basis of the tangent space at each point of an open set U ⊂ M.