# Curvature /Torsion of space curve on Surface/3-space

Given geodesic curvature and torsion $\kappa_g,\tau_g$ on a surface as functions of arc, how to compute (stand alone $\mathbb R^3$embedded ) curvature and torsion $\kappa,\tau$?

Are the following correct/relevant in this context ? I did not see them in printed on same page of any text. $\gamma$ is angle between total vector and normal.

EDIT 1 (typo):

$\kappa_n = \kappa \cos \gamma$ ( Meusnier thm )

same as

$\kappa_g = \kappa_n \tan \gamma$ ( also Meusnier thm )

and

$\tau_g = \tau + \dfrac{d \gamma}{ds}$ (Joachimsthal thm?)