Magnetic systems are the natural toy model for the motion of a charged particle moving on a Riemannian manifold under the influence of a (static) magnetic force. In this talk we introduce a curvature operator called magnetic curvature which encodes the information of the classical Riemannian curvature together with terms of perturbation due to the magnetic interaction. In a variational setting, we use this new notion of curvature to approach the problem of finding closed trajectories. 
org: PROCESI Michela