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arXiv · 1009.1175

Codimension one symplectic foliations and regular Poisson structures

Victor Guillemin·Eva Miranda·Ana Rita Pires
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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 Poisson b-manifold as we consider in a later paper.

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Victor Guillemin, Eva Miranda, Ana Rita Pires. 2010-09-06. Codimension one symplectic foliations and regular Poisson structures. https://arxiv.org/abs/1009.1175

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