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arXiv · 2201.02258

Magnetic trajectories on 2-step nilmanifolds

Gabriela P. Ovando·Mauro Subils
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Abstract

The aim of this work is the study of magnetic trajectories on nilmanifolds. The magnetic equation is written and the corresponding solutions are found for a family of invariant Lorentz forces on a 2-step nilpotent Lie group equipped with a left-invariant metric. Some examples are computed in the Heisenberg Lie groups $H_n$ for $n=3,5$, showing differences with the case of exact forms. Interesting magnetic trajectories related to elliptic integrals appear in $H_3$. The question of existence of closed or periodic magnetic trajectories for every energy level on Lie groups or on compact quotients is treated.

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Gabriela P. Ovando, Mauro Subils. 2022-01-06. Magnetic trajectories on 2-step nilmanifolds. https://arxiv.org/abs/2201.02258

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