On the moment map on symplectic manifolds

Details On the moment map on symplectic manifolds On the moment map on symplectic manifolds

2006-05-10

arxiv.org/abs/math/0605270v3

Mathematics

Differential Geometry

v.1: 8 pages. v.2, 9 pages: Theorem 1.1 is corrected and improved. Proposition 1.2 (v.1) becomes Theorem 1.2 and it is improve

Scientific paper

We consider a connected symplectic manifold $M$ acted on by a connected Lie group $G$ in a Hamiltonian fashion. If $G$ is compact, we prove give an Equivalence Theorem for the symplectic manifolds whose squared moment map $\parallel \mu \parallel^2$ is constant. This result works also in the almost-K\"ahler setting. Then we study the case when $G$ is a non compact Lie group acting properly on $M$ and we prove a splitting results for symplectic manifolds.

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