Periodic orbits in magnetic fields and Ricci curvature of Lagrangian systems

1998/01/01 by Abbas Bahri, Iskander Taimanov, I. A. Taĭmanov · 8 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.1090/s0002-9947-98-02108-4

Abstract

A Lagrangian system describing a motion of a charged particle on a Riemannian manifold is studied. For this flow an analog of a Ricci curvature is introduced, and for Ricci positively curved flows the existence of periodic orbits is proved.

Cited by

• Magnetic vortex filament flows
• A bifurcation result for semi-Riemannian trajectories of the Lorentz force equation
• Existence of curves with constant geodesic curvature in a Riemannian 2-sphere
• Electromagnetic curvature via Jacobi-Maupertuis and beyond
• Infinitely many noncontractible closed magnetic geodesics on non-compact manifolds
• Periodic orbits of Hamiltonian flows near symplectic critical submanifolds
• Periodic motion of a charge on a manifold in the magnetic fields
• Magnetic Flatness and E. Hopf's Theorem for Magnetic Systems. [europepmc]

Related

• Periodic motion of a charge on a manifold in the magnetic fields
• Periodic orbits of Hamiltonian flows near symplectic critical submanifolds
• Magnetic curvature and existence of a closed magnetic geodesic on low energy levels
• Periodic orbits of Hamiltonian flows near symplectic extrema
• Non-contractible periodic orbits of Hamiltonian flows on twisted cotangent bundles