Round Morse functions and isoenergy surfaces of integrable Hamiltonian systems

A study is made of the topology of a class of three-dimensional manifolds that arise as constant energy surfaces for integrable systems. It is proved that this class coincides with the class of manifolds admitting a function all of whose critical manifolds are nondegenerate circles and whose nonsingular level surfaces are disjoint unions of tori. Necessary and sufficient conditions are obtained for the existence of minimal round Morse functions on manifolds of dimension greater than five.
Figures: 3.
Bibliography: 20 titles.