Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 048, 23 pages      arXiv:2301.09075      https://doi.org/10.3842/SIGMA.2023.048

Koenigs Theorem and Superintegrable Liouville Metrics

Galliano Valent
Laboratoire de Physique Mathématique de Provence, 12 Rue Fabrot, 13100 Aix-en-Provence, France

Received January 26, 2023, in final form July 08, 2023; Published online July 19, 2023

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.

Key words: Koenigs metrics; Liouville metrics; superintegrable geodesic flows; two-dimensional manifolds.

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