Frictional magnetic curves in 3D Riemannian manifolds

In this study, we investigate the special type of magnetic trajectories associated with a magnetic field B defined on a 3D Riemannian manifold. First, we consider a moving charged particle under the action of a frictional force, f, in the magnetic field B. Then, we assume that trajectories of the particle associated with the magnetic field B correspond to frictional magnetic curves (f-magnetic curves) of magnetic vector field B on the 3D Riemannian manifold. Thus, we are able to investigate some geometrical properties and physical consequences of the particle under the action of frictional force in the magnetic field B on the 3D Riemannian manifold.