2010/09/30 by Victor Guillemin, Eva Miranda, Ana Rita Pires · 1 citation
Mathematics · Physics and Astronomy · #math.SG #math-ph #math.DG #math.MP #msc:53D17 #msc:53C12
published as Bull. Braz. Math. Soc. (N.S.) 42 (2011), no. 4, 607-623 · 17 pages; revised version, some references added, proofs of propositions 15 and 18 revised, examples in section 3.3 added
arxiv created 2011/06/21 · arxiv updated 2015/09/09
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.