Factorization Way to Symmetries of Systems on Curved Spaces

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.