Killing submersions and magnetic curves

Abstract

We investigate magnetic curves in Killing submersions and we show that the bundle curvature is constant along magnetic curves with respect to the Killing vector field if and only if all vertical tubes derived from these magnetic curves are of constant mean curvature. Then we examine magnetic Jacobi fields along horizontal Killing magnetic curves in the total space of a Killing submersion. We generalize some important results obtained by O'Neill for horizontal geodesics to horizontal magnetic curves. Finally, we study magnetic Jacobi fields along horizontal Killing magnetic trajectories in 3-dimensional Sasakian space forms.