If I have a regular curve such that $\boldsymbol{r}(s)=\boldsymbol{n}(s)$ for all $s$, how can i find curvature and torsion?
It is easy to see that $\|\boldsymbol{r}(s)\|=1$. Therefore, the trace of the curve is over a unitary sphere, but i can't find curvature and torsion. It is possible to find it?
HINT:
As always, assume an arclength parametrization (so $s$ is arclength) and differentiate and see what the Frenet formulas tell you. Remember to use the fact that $\mathbf t,\mathbf n,\mathbf b$ give a basis. This is almost always the right approach when working with curves ...