Codimension one symplectic foliations and regular Poisson structures

Details Codimension one symplectic foliations and regular Poisson structures Codimension one symplectic foliations and regular Poisson structures

2010-09-06

arxiv.org/abs/1009.1175v2

Mathematics

Symplectic Geometry

17 pages; revised version, some references added, proofs of propositions 15 and 18 revised, examples in section 3.3 added

Scientific paper

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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