A completely integrable Hamiltonian system of C. Neumann-type on the complex projective space (Q1097562)

A complete integrability of the Hamiltonian system that describes the motion of a point on the complex projective space \(P^{n-1}\) under the influence of a potential \(\sum a_ jIz_ jI\) 2 is proved and appropriate independent integrals in involution are constructed. The problem is a generalization of the famous problem by C. Neumann on the motion of a point on the sphere \(S^{n-1}\) under the influence of a quadratic potential \(\sum a_ jx\) \(2_ j\).