Codimension one symplectic foliations and regular Poisson manifolds
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...
| Autores: | , , |
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 2010 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/9840 |
| Acceso en línea: | https://hdl.handle.net/2117/9840 |
| Access Level: | acceso abierto |
| Palabra clave: | Foliations (Mathematics) Foliacions (Matemàtica) Topologia diferencial Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial |
| Sumario: | 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 [GMP]. |
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