Gravitational magnetic curves on 3D Riemannian manifolds

In this paper, we study a special type of magnetic trajectories associated with a magnetic field B defined on a 3D Riemannian manifold. First, we assume that we have a moving charged particle which is supposed to be under the action of a gravitational force G in the magnetic field B on the 3D Riemannian manifold. Then, we determine trajectories of the charged particle associated with the magnetic field B and we define gravitational magnetic curves (G-magnetic curves) of the magnetic vector field B on the 3D Riemannian manifold. Finally, we investigate some geometrical and physical features of the moving charged particle corresponding to the G-magnetic curve. Namely, we compute the energy, magnetic force, and uniformity of the G-magnetic curve.