Existence of contractible closed magnetic geodesics proven on Heisenberg nilmanifolds below Mañé critical value, with lattice conditions for closed projections and examples of quotients with infinitely many or no non-contractible trajectories.
Eberlein , Geometry of 2-step nilpotent Lie groups with a left-invaria nt metric , Ann
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Closed Magnetic geodesics on Heisenberg nilmanifolds
Existence of contractible closed magnetic geodesics proven on Heisenberg nilmanifolds below Mañé critical value, with lattice conditions for closed projections and examples of quotients with infinitely many or no non-contractible trajectories.