Particles with curvature and torsion in three-dimensional pseudo-Riemannian space forms

We consider the motion of relativistic particles described by an action which is a function of the curvature and torsion of the particle path. The Euler–Lagrange equations and the dynamical constants of the motion are expressed in a simple way in terms of a suitable coordinate system. The moduli spaces of solutions in a three-dimensional pseudo-Riemannian space form are completely exhibited.