The preceding chapters presented various procedures that led to the construction of new symplectic manifolds from Poisson or symplectic manifolds acted canonically upon by a Lie group. The present goal is the description of a general method to obtain new Poisson manifolds, or at least Poisson algebras, by reducing symmetric Poisson manifolds. In parallel, we will show the relationship between these reduced spaces and the symplectic reduced spaces that were previously introduced. References related to this topic are Marsden and Ratiu (1986), Vaisman (1996b), and Ortega and Ratiu (1998).
KeywordsOpen Neighborhood Poisson Bracket Symplectic Form Symplectic Manifold Poisson Structure
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