Factorization Way to Symmetries of Systems on Curved Spaces

TL;DR

This paper extends the factorization method for identifying symmetries from flat to curved spaces, analyzing systems like Kepler-Coulomb and Oscillator in constant curvature environments.

Contribution

It demonstrates how to apply the factorization approach to curved spaces and extends it to specific superintegrable systems such as SW and Evans models.

Findings

Factorization method successfully applied to curved space systems.

Symmetries of Kepler-Coulomb and Oscillator systems characterized in curved spaces.

Extension of the method to additional superintegrable systems.

Abstract

In a previous work we showcased the factorization method to find the symmetries of superintegrable systems with spherical separability in flat spaces. Here we analyze the same problem, but in constant curvature spaces along the examples of curved Kepler-Coulomb and Harmonic Oscillator systems. We also show how this procedure can also be directly extended to the curved Smorodinsky-Winternitz (SW) and Evans systems.