  A Poisson coalgebra analogue of a (non-standard) quantum deformation of sl(2)
is shown to generate an integrable geodesic dynamics on certain 2D spaces of
non-constant curvature. Such a curvature depends on the quantum deformation
parameter z and the flat case is recovered in the limit z\to 0. A
superintegrable geodesic dynamics can also be defined in the same framework,
and the corresponding spaces turn out to be either Riemannian or relativistic
spacetimes (AdS and dS) with constant curvature equal to z. The underlying
coalgebra symmetry of this approach ensures the existence of its generalization
to arbitrary dimension.
