Codimension one symplectic foliations and regular Poisson structures
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Guillemin_Codimension one.pdf
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203.57 KB
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Author(s)
Miranda, Eva
Guillemin, Victor W.
Pissarra Pires, Ana Rita
Date Issued
December 2011
Journal
Bulletin of the Brazilian Mathematical Society, New Series
Publisher
Springer-Verlag
Citation
Guillemin, Victor, Eva Miranda, and Ana Rita Pires. “Codimension one symplectic foliations and regular Poisson structures.” Bulletin of the Brazilian Mathematical Society, New Series 42, no. 4 (December 3, 2011): 607-623.
Version
Original manuscript
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].
Description
Original manuscript June 21, 2011
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1007/s00574-011-0031-6
