Frictional magnetic curves in 3D Riemannian manifolds

Abstract

In this study, we investigate the special type of magnetic trajectories associated with a magnetic field 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. Then, we assume that trajectories of the particle associated with the magnetic field correspond to frictional magnetic curves (f-magnetic curves) of magnetic vector field 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 on the 3D Riemannian manifold. © 2018 World Scientific Publishing Company.