Superintegrability on the hyperbolic plane with integrals of any degree \(\geq 2\)

DOI10.1016/j.geomphys.2022.104686zbMath1505.32015OpenAlexW4305042281WikidataQ115574739 ScholiaQ115574739MaRDI QIDQ2107511

Galliano Valent

Publication date: 1 December 2022

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2022.104686

zbMATH Keywords

closed geodesicstwo-dimensional closed manifoldsZoll metrics

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Real-analytic manifolds, real-analytic spaces (32C05)

Cites Work

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• Zoll and Tannery metrics from a superintegrable geodesic flow
• Explicit metrics for a class of two-dimensional cubically superintegrable systems
• Two-dimensional superintegrable metrics with one linear and one cubic integral
• Examples of complete solvability of 2D classical superintegrable systems
• Invariant characterization of Liouville metrics and polynomial integrals
• Superintegrable models on Riemannian surfaces of revolution with integrals of any integer degree. I
• Superintegrable geodesic flows versus Zoll metrics
• Global structure and geodesics for Koenigs superintegrable systems
• Superintegrability in a two-dimensional space of nonconstant curvature
• Superintegrable systems in Darboux spaces

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