Periodic orbits in magnetic fields and Ricci curvature of Lagrangian systems

Details Periodic orbits in magnetic fields and Ricci curvature of Lagrangian systems Periodic orbits in magnetic fields and Ricci curvature of Lagrangian systems

1995-11-30

arxiv.org/abs/dg-ga/9511016v2

Trans. Amer. Math. Soc. 350 (1998), 2697-2717.

Mathematics

Differential Geometry

AMSTeX, 22 pages

Scientific paper

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.

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