Coupling Tensors and Poisson Geometry Near a Single Symplectic Leaf
| dc.creator | Vorobjev, Yurii | |
| dc.date | 2000-08-22 | |
| dc.date | 2000-11-11 | |
| dc.date.accessioned | 2026-07-07T04:36:54Z | |
| dc.date.available | 2026-07-07T04:36:54Z | |
| dc.description | In the framework of the connection theory, a contravariant analog of the Sternberg coupling procedure is developed for studying a natural class of Poisson structures on fiber bundles, called coupling tensors. We show that every Poisson structure near a closed symplectic leaf can be realized as a coupling tensor. Our main result is a geometric criterion for the neighborhood equivalence between Poisson structures over the same leaf. This criterion gives a Poisson analog of the relative Darboux theorem due to Weinstein. Within the category of the algebroids, coupling tensors are introduced on the dual of the isotropy of a transitive Lie algebroid over a symplectic base. As a basic application of these results, we show that there is a well defined notion of a ``linearized'' Poisson structure over a symplectic leaf which gives rise to a natural model for the linearization problem. | |
| dc.description | 31 pages, LaTex, Lecture at "Poisson 2000", CIRM, Luminy, France, 26-30, 2000 | |
| dc.identifier | https://arxiv.org/abs/math/0008162 | |
| dc.identifier | http://arxiv.org/abs/math/0008162 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59772 | |
| dc.subject | Symplectic Geometry | |
| dc.title | Coupling Tensors and Poisson Geometry Near a Single Symplectic Leaf | |
| dc.type | text |