Codimension one symplectic foliations and regular Poisson structures |
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Authors: | Victor Guillemin Eva Miranda Ana Rita Pires |
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Institution: | 1. Department of Mathematics, Massachussets Institute of Technology, Cambridge, MA, USA 2. Departament de Matem??tica Aplicada I, Universitat Polit??cnica de Catalunya, Barcelona, Spain 3. Department of Mathematics, Massachussets Institute of Technology, Cambridge, MA, USA
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Abstract: | In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending the symplectic form on each leaf. If such a manifold has a compact leaf, then all the leaves are compact, and furthermore the manifold is a mapping torus of a compact leaf. These manifolds and their regular Poisson structures admit an extension as the critical hypersurface of a b-Poisson manifold as we will see in 9]. |
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