# Curves Problems

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