Superintegrable metrics on surfaces admitting integrals of degrees 1 and 4

2018/05/26 by Pavel P. Novichkov, Novichkov, Pavel
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.1805.10439

openalex publication_date 2018/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Riemannian metrics on surfaces whose geodesic flows are superintegrable with one integral linear in momenta and one integral quartic in momenta. The main results of the work are local description of such metrics in terms of ordinary differential equations, integration of the equations, and description of the corresponding Poisson algebra of integrals of motion. We also give examples of such metrics that can be extended to the sphere S², and study the group of symmetries of the problem.

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