Koenigs Theorem and Superintegrable Liouville Metrics - Valent, Galliano (Symmetry, Integrability and Geometry: Methods and Applications, 2023)
In the first part, we give a new proof of Koenigs theorem and, in the second part, we determine the local form of all the superintegrable Riemannian Liouville metrics as well as their global geometries.