Magnetic trajectories on 2-step nilmanifolds

2022/01/06 by Gabriela P. Ovando, Ovando, Gabriela P., Mauro Subils +1 · 1 citation
Physics and Astronomy · #22E25 #53C99 #70G45 #70G65 #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2201.02258

openalex publication_date 2022/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 H₃. 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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