ON SOME SYMPLECTIC GROUP ACTIONS WHERE ALL THE ORBITS ARE EQUIVARIANTLY ISOMORPHIC AND DIFFEOMORPHIC TO A FIXED ORBIT OF THE COADJOINT ACTION

Abstract

In conformity with the 'Foundations of Mechanics' given by R. ABRAHAM and J. E. MARSDEN [1] let (P,w) be a symplectic manifold and Φ:GxP-P a Hamiltonian action of a compact, connected Lie group G on the manifold P. Considering this setting J. SZENTHE [2] found the following result: If the isotropy subgroups of the action Φ are of maximal rank then all the orbits of Φ are equivariantly isomorphic. Consequently, P is the total space of a differentiable fibre bundle, where the base manifold is the orbit space of the action Φ and the fibres are diffeomorphic to a fixed orbit of the coadjoint action. The aim of the present paper is to develop further characterizations of the above situation as it was suggested by J. J. DUISTERMAAT.