Moving frame

Summary

A moving frame is a basis of the tangent space that varies smoothly from point to point. It may live on a manifold or along a curve or surface. Élie Cartan developed the method of moving frames. One expresses the derivatives of the frame in terms of the frame itself, and the coefficients become the invariants of the geometry. The Frenet frame of a space curve, whose derivative gives curvature and torsion, is the classical example. In modern terms a moving frame is a local section of the frame bundle.