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On the moment map on symplectic manifolds

Leonardo Biliotti
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Abstract

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 $\parallel μ\parallel^2$ is constant. This result works also in the almost-Kähler 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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Leonardo Biliotti. 2006-09-28. On the moment map on symplectic manifolds. https://arxiv.org/abs/math/0605270

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