I have three problems that I'm really stuck on. Perhaps someone could give me a pointer on how to start, I literally have no idea, but perhaps a step or two would help.
1) Prove that an arc-length parametrised curve is planar iff it has an adapted frame such that .
2) Prove that any two parallel frames of a curve are related by a constant rotation in the normal plane.
3) Express curvature and torsion of a Frenet curve in terms of and of a parallel frame, and vice versa.