Classification of Killing magnetic curves in H3

Abstract

In this paper, we study classification of magnetic curves corresponding to Killing vector fields of H-3. First, we solve the geodesic equation analytically. Then we calculate the trajectories generated by all the six Killing vector fields, which are considered as magnetic field vectors, by using perturbation method up to first-order with respect to the strength of the magnetic field. We present a comparison of our solution with the numerical solution for one case. We also prove that 3-dimensional (alpha)-Kenmotsu manifolds cannot have any magnetic vector field in the direction of their Reeb vector fields.