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

2025/06/29 by Alexey V. Bolsinov, Bolsinov, Alexey V., Andrey Yu. Konyaev +3 · 1 citation
Mathematics · #37J35 #70H06 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #Navier-Stokes equation solutions

paper · doi:10.48550/arxiv.2506.23312

openalex publication_date 2025/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a recent conjecture of Dragovic et al arXiv2504.20515 stating that the magnetic geodesic flow on the standard sphere Sⁿ⊂ \mathbb Rⁿ⁺¹ whose magnetic 2-form is the restriction of a constant 2-form from ℝⁿ⁺¹ is Liouville integrable. The integrals are quadratic and linear in momenta.

Citations

• A Lax representation and integrability of homogeneous exact magnetic flows on spheres in all dimensions
• Integrability of homogeneous exact magnetic flows on spheres
• Orthogonal separation of variables for spaces of constant curvature
• Separation coordinates, moduli spaces and Stasheff polytopes

Cited by

• A Lax representation and integrability of homogeneous exact magnetic flows on spheres in all dimensions
• Contact magnetic geodesic and sub-Riemannian flows on V_n,2 and integrable cases of a heavy rigid body with a gyrostat

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