A recently introduced set of N-dimensional quasi-maximally superintegrable Hamiltonian systems describing geodesic motions that can be used to generate "dynamically" a large family of curved spaces is revisited. From an algebraic viewpoint, such spaces are obtained through kinetic energy Hamiltonians defined on either the sl(2) Poisson coalgebra or a quantum deformation of it. Certain potentials on these spaces and endowed with the same underlying coalgebra symmetry have also been introduced in such a way that the superintegrability properties of the full system are preserved. Several new N = 2 examples of this construction are explicitly given, and specific Hamiltonians leading to spaces of nonconstant curvature are emphasized.
Ballesteros, A., Herranz, F.j., Ragnisco, O. (2008). Superintegrability on sl(2)-coalgebra spaces RID F-2453-2010. PHYSICS OF ATOMIC NUCLEI, 71(5), 812-818 [10.1134/S1063778808050074].