Curvature decomposition for a spherical curve
= Curvature decomposition for a spherical curve
For a unit-speed curve on the unit sphere,
$$
\alpha=-\kappa^{-1}n-\tau^{-1}\kappa^{-2}\dot\kappa\,b,
\qquad
\kappa_g=-\kappa^{-1}\tau^{-1}\dot\kappa
$$
under the compatible signed-torsion and geodesic-curvature conventions.