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0737.58022
Gotay,
M.J.; Tuynman,
G.M.
A symplectic analogue of the Mostow-Palais theorem. (English)
[CA] Symplectic geometry, groupoids, and integrable systems, Sémin.
Sud- Rhodan. Geom. VI, Berkeley/CA (USA) 1989, Math. Sci. Res. Inst. Publ.
20, 173-182 (1991).
The paper proves the following theorem: Let a Lie group $G$ act on a compact
connected symplectic manifold $(M,\omega)$ of finite type by symplectomorphisms.
If the action has a momentum map then $(M,G,\omega)$ can be obtained as
an equivariant reduction of some $\bbfR\sp n$ with the standard symplectic
structure. Moreover, the action of $G$ on $\bbfR\sp n$ may be the cotangent
lift of an orthogonal action on $\bbfR\sp n$.
[ C.Günther
(Libby) ]
Keywords: symplectic actions; Hamiltonian $G$-space; symplectic manifold