Periodic orbits in magnetic fields and Ricci curvature of Lagrangian systems

Abstract

We consider a periodic problem for the motion of a charged particle in a magnetic field. Introducing a notion of Ricci curvature for such Lagrangian systems and using the methods of the calculus of variations in the large, we prove the existence of periodic motions for such particles under a condition of positivity of the Ricci curvature.

arXiv commentAMSTeX, 22 pages