2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/179770An 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.11 pages. Comments and new references have been added; expressions for scalar curvatures have been corrected and simplifiedHigh Energy Physics - TheoryMathematical Physicstext