  An infinite family of ND spaces endowed with sl(2)-coalgebra symmetry is
introduced. For all these spaces the geodesic flow is superintegrable, and the
explicit form of their common set of integrals is obtained from the underlying
sl(2)-coalgebra structure. In particular, ND spherically symmetric spaces with
Euclidean signature are shown to be sl(2)-coalgebra spaces. As a byproduct of
this construction we present ND generalizations of the classical Darboux
surfaces, thus obtaining remarkable superintegrable ND spaces with non-constant
curvature.
