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