Classification des actions hamiltoniennes complètement intégrables de rang deux. (Classification of completely integrable Hamiltonian actions of rang 2.) (Q923450)

According to the definition of \textit{A. S. \textit{Mishchenko}} and \textit{A. T. Fomenko} [Funkts. Anal. Prilozh. 12, No.2, 46-56 (1978; Zbl 0396.58003)] the action of a Lie group G is completely integrable if it is locally free in a point, at least, and if the dimension of the manifold is the sum of the dimension and the rank of G. This highly abstract paper presents the proof of the following theorem. Let G be a compact connected Lie group of rank two, and \(M_ 1\) and \(M_ 2\) two manifolds on which the action of G is completely integrable; assume that these manifolds have the same image by the moment map, and that their principal isotropy groups are the same, then there exists a symplectic G-equivariant isomorphism of one onto the other.