
Curves Problems
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 arclength parametrised curve $\displaystyle y(s)$ is planar iff it has an adapted frame such that $\displaystyle \kappa_n = \tau = 0$.
2) Prove that any two parallel frames of a curve $\displaystyle y(t)$ are related by a constant rotation in the normal plane.
3) Express curvature and torsion of a Frenet curve in terms of $\displaystyle \kappa_n$ and $\displaystyle \kappa_g$ of a parallel frame, and vice versa.
Thanks!