This article is cited in 18 papers

Round Morse functions and isoenergy surfaces of integrable Hamiltonian systems

S. V. Matveev, A. T. Fomenko, V. V. Sharko


Abstract: 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.

UDC: 513.944

MSC: Primary 58F05, 58F07, 57R65; Secondary 70H10

Received: 10.07.1986

 English version: Mathematics of the USSR-Sbornik, 1989, 63:2, 319–336

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