Koenigs Theorem and Superintegrable Liouville Metrics

TL;DR

This paper provides a new proof of Koenigs theorem and classifies all superintegrable Liouville metrics on Riemannian surfaces, detailing their local forms and global geometries.

Contribution

It offers a novel proof of Koenigs theorem and completely characterizes superintegrable Liouville metrics, including their local and global geometric properties.

Findings

New proof of Koenigs theorem

Classification of superintegrable Liouville metrics

Description of local forms and global geometries

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.