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arXiv · 2506.23312

Integrability of the magnetic geodesic flow on the sphere with a constant 2-form

Alexey V. Bolsinov·Andrey Yu. Konyaev·Vladimir S. Matveev
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Abstract

We prove a recent conjecture of Dragovic et al arXiv2504.20515 stating that the magnetic geodesic flow on the standard sphere $S^n\subset \mathbb R^{n+1}$ whose magnetic 2-form is the restriction of a constant 2-form from $\mathbb{R}^{n+1}$ is Liouville integrable. The integrals are quadratic and linear in momenta.

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Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev. 2025-06-29. Integrability of the magnetic geodesic flow on the sphere with a constant 2-form. https://doi.org/10.1142/s0219887826500416

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