In this paper (arXiv:1310.6554) a new maximally superintegrable deformation of the N-dimensional Kepler–Coulomb Hamiltonian is presented. From a geometric viewpoint, this superintegrable Hamiltonian can be interpreted as a system on an N-dimensional Riemannian space with nonconstant curvature. The eigenvalues and eigenfunctions of the model are explicitly obtained, and the spectrum presents a hydrogen-like shape for positive values of the deformation parameter and of the corresponding coupling constant.