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arXiv · 2002.06982

Periodic Magnetic Geodesics on Heisenberg Manifolds

Jonathan Epstein·Ruth Gornet·Maura B. Mast
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Abstract

We study the dynamics of magnetic flows on Heisenberg groups. Let $H$ denote the three-dimensional simply connected Heisenberg Lie group endowed with a left-invariant Riemannian metric and an exact, left-invariant magnetic field. Let $\Gamma$ be a lattice subgroup of $H,$ so that $\Gamma\backslash H$ is a closed nilmanifold. We first find an explicit description of magnetic geodesics on $H$, then determine all closed magnetic geodesics and their lengths for $\Gamma \backslash H$. We then consider two applications of these results: the density of periodic magnetic geodesics and marked magnetic length spectrum rigidity.

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Jonathan Epstein, Ruth Gornet, Maura B. Mast. 2020-02-17. Periodic Magnetic Geodesics on Heisenberg Manifolds. https://arxiv.org/abs/2002.06982

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