A maximally superintegrable system on an n-dimensional space of nonconstant curvature RID F-2453-2010

We present a novel Hamiltonian system in n dimensions which admits the maximal number 2n - 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. (c) 2007 Elsevier B.V. All rights reserved