Periodic orbits in magnetic fields and Ricci curvature of Lagrangian systems

@inproceedings{Bahri1995PeriodicOI,
  title={Periodic orbits in magnetic fields and Ricci curvature of Lagrangian systems},
  author={Abbas Bahri and I. A. Taimanov},
  year={1995}
}
where dA -F, on the space of closed curves on the manifold Mn. Here A is a 1-form (i.e., F is an exact 2-form). This functional is a natural generalization of the usual functional of length, and its closed extremals correspond to periodic trajectories of the motion of particles on the Riemannian manifold Mn when the kinetic energy is defined by the metric tensor and the form F defines a magnetic field. Also this functional corresponds to the periodic orbits for other problems of classical… CONTINUE READING

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