Critical curves for a Santalَ problem in 3-space forms

L. Santalَ (1956) studied in [15] the minimization of Frenet first curvature dependent energies for spaces of curves constrained to lie in a surface of the euclidean 3-space. In this paper we analyze an extension of that problem by considering energy functionals, determined by Lagrangians which depend not only on the curvature but also on the torsion, acting on spaces of surface contained clamped curves of real 3-space forms.