We consider a connected symplectic manifold M acted on properly and in a Hamiltonian fashion by a connected Lie group G. If G is compact, then we characterize the symplectic manifolds whose squared moment map is constant. We also give a sufficient condition for G to admit a symplectic orbit. Then we study the case when G is a non-compact Lie group proving splitting results for symplectic manifolds

On the moment map on symplectic manifolds / BILIOTTI L.. - In: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY SIMON STEVIN. - ISSN 1370-1444. - 16(2009), pp. 107-116.

On the moment map on symplectic manifolds

BILIOTTI, Leonardo
2009

Abstract

We consider a connected symplectic manifold M acted on properly and in a Hamiltonian fashion by a connected Lie group G. If G is compact, then we characterize the symplectic manifolds whose squared moment map is constant. We also give a sufficient condition for G to admit a symplectic orbit. Then we study the case when G is a non-compact Lie group proving splitting results for symplectic manifolds
On the moment map on symplectic manifolds / BILIOTTI L.. - In: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY SIMON STEVIN. - ISSN 1370-1444. - 16(2009), pp. 107-116.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2286396
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