GEOMETRICAL ASPECTS OF MOTION OF CHARGED PARTICLES IN MAGNETIC AND KILLING MAGNETIC FIELDS AND THEIR CORRESPONDING TRAJECTORIES IN ANTI-DE SITTER 3-SPACE

We inquire the motion of charged particles varying under the effect of Lorentz force produced by magnetic and Killing magnetic fields in anti-de Sitter 3-space H-1(3). Primarily, we characterize magnetic trajectories in H-1(3) in terms of their Frenet apparatus. Thereafter, utilizing a geometrical model of split-quaternions for H-1(3) (where H-1(3) corresponds to a subspace of the Lie group H of split-quaternions) we find 6 independent unit Killing vector fields on H-1(3) which constitutes a basis for the corresponding 6D Lie algebra i(H-1(3)). We conclude with characterizations of Killing magnetic trajectories in H-1(3) with respect to quasi-slope, curvature and torsion or pseudo-torsion (depending on the situation).