A maximally superintegrable system on an -dimensional space of nonconstant curvature

We present a novel Hamiltonian system in n dimensions which admits the maximal number 2 n − 1 of functionally independent, quadratic first integrals. This system turns out to be the first example of a maximally superintegrable Hamiltonian on an n -dimensional Riemannian space of nonconstant curvature, and it can be interpreted as the intrinsic Smorodinsky–Winternitz system on such a space. Moreover, we provide three different complete sets of integrals in involution and solve the equations of motion in closed form.