Codimension one symplectic foliations and regular Poisson structures
Symplectic Geometry
2015-09-09 v2 Mathematical Physics
Differential Geometry
math.MP
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.
Cite
@article{arxiv.1009.1175,
title = {Codimension one symplectic foliations and regular Poisson structures},
author = {Victor Guillemin and Eva Miranda and Ana Rita Pires},
journal= {arXiv preprint arXiv:1009.1175},
year = {2015}
}
Comments
17 pages; revised version, some references added, proofs of propositions 15 and 18 revised, examples in section 3.3 added