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Symmetry, Integrability and Geometry: Methods and Applications, 2023, Volume 19, 048, 23 pp.
DOI: https://doi.org/10.3842/SIGMA.2023.048 (Mi sigma1943) 		 
Koenigs Theorem and Superintegrable Liouville Metrics

Galliano Valent

Laboratoire de Physique Mathématique de Provence, 12 Rue Fabrot, 13100 Aix-en-Provence, France
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DOI: https://doi.org/10.3842/SIGMA.2023.048
Abstract: In a first part, we give a new proof of Koenigs theorem and, in a second part, we determine the local form of all the superintegrable Riemannian Liouville metrics as well as their global geometries.
Keywords: Koenigs metrics, Liouville metrics, superintegrable geodesic flow, two-dimensional manifolds.
Received: January 26, 2023; in final form July 8, 2023; Published online July 19, 2023
Document Type: Article
MSC: 32C05, 37E35, 37E99, 37J35
Language: English
Citation: Galliano Valent, “Koenigs Theorem and Superintegrable Liouville Metrics”, SIGMA, 19 (2023), 048, 23 pp.
Citation in format AMSBIB
\Bibitem{Val23}
\by Galliano~Valent
\paper Koenigs Theorem and Superintegrable Liouville Metrics
\jour SIGMA
\yr 2023
\vol 19
\papernumber 048
\totalpages 23
\mathnet{http://mi.mathnet.ru/sigma1943}
\crossref{https://doi.org/10.3842/SIGMA.2023.048}
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