Miguel Angel Javaloyes

Departamento de Matemáticas, Universidad de Murcia

Relativistic particles with curvature and torsion in three-dimensional space forms
We consider the motion of relativistic particles described by an action depending on an arbitrary function on the curvature and torsion in three-dimensional space forms. The Euler-Lagrange equations and the dynamical constants of the motion associated with the symmetry groups are expressed in a very simple form in terms of the curvatures of the embedded worldline. By using the Killing fields related to the Noether Theorem, we are able to integrate the Euler-Lagrange equations, finding the curvature and torsion of the critical points in some interesting cases. Finally, by choosing a suitable coordinate system, we obtain the critical curves in terms of its curvatures.