  An N-dimensional position-dependent mass Hamiltonian (depending on a
parameter \lambda) formed by a curved kinetic term and an intrinsic oscillator
potential is considered. It is shown that such a Hamiltonian is exactly
solvable for any real positive value of the parameter \lambda. Algebraically,
this Hamiltonian can be thought of as a new maximally superintegrable
\lambda-deformation of the N-dimensional isotropic oscillator and, from a
geometric viewpoint, this system is just the intrinsic oscillator potential on
an N-dimensional hyperbolic space with nonconstant curvature. The spectrum of
this model is shown to be hydrogenlike, and their eigenvalues and
eigenfunctions are explicitly obtained by deforming appropriately the symmetry
properties of the N-dimensional harmonic oscillator. A further generalization
of this construction giving rise to new exactly solvable models is envisaged.
