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Article Dans Une Revue Letters in Mathematical Physics Année : 2004

Symmetry Reduction in Symplectic and Poisson Geometry

Tudor S. Ratiu
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Résumé

We present a quick review of several reduction techniques for symplectic and Poisson manifolds using local and global symmetries compatible with these structures. Reduction based on the standard momentum map (symplectic or Marsden–Weinstein reduction) and on generalized distributions (the optimal momentum map and optimal reduction) is emphasized. Reduction of Poisson brackets is also discussed and it is shown how it defines induced Poisson structures on cosymplectic and coisotropic submanifolds.

Dates et versions

hal-00023623 , version 1 (02-05-2006)

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Juan-Pablo Ortega, Tudor S. Ratiu. Symmetry Reduction in Symplectic and Poisson Geometry. Letters in Mathematical Physics, 2004, 69, pp.11-60. ⟨10.1007/s11005-004-0898-x⟩. ⟨hal-00023623⟩
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