Find a curve $\vec{r(s)}^{\,}$ with arc length parameter $s$ whose locus of centers of spherical curvature is $\vec{r^{*}(s)}^{\,} = (cos s, sin s, s).$
I tried using the result that product of corresponding torsions and radii of curvature are equal. But I couldn't reach anywhere. Please if anybody could give me any idea, it will be helpful. Thanks a lot in advance.