A new approach for magnetic curves in 3D Riemannian manifolds

A magnetic field is defined by the property that its divergence is zero in a three-dimensional oriented Riemannian manifold. Each magnetic field generates a magnetic flow whose trajectories are curves called as magnetic curves. In this paper, we give a new variational approach to study the magnetic flow associated with the Killing magnetic field in a three-dimensional oriented Riemann manifold, (M3, g). And then, we investigate the trajectories of the magnetic fields called as N-magnetic and B-magnetic curves.