On the moment map on symplectic manifolds

Leonardo Biliotti

On the moment map on symplectic manifolds

Differential Geometry 2007-05-23 v3

Authors: Leonardo Biliotti

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 $\parallel \mu \parallel^2$ 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.

Keywords

symplectic geometry group actions on manifolds lie groups

Cite

@article{arxiv.math/0605270,
  title  = {On the moment map on symplectic manifolds},
  author = {Leonardo Biliotti},
  journal= {arXiv preprint arXiv:math/0605270},
  year   = {2007}
}

Comments

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 improved. Proposition 1.3 completely revisited, due a crucial error in the proof. Finally, Corollary 1.4 did not appear in v.1. v.3 some mistakes are corrected

On the moment map on symplectic manifolds

Abstract

Keywords

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