Poisson structures on tangent bundles

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dc.creatorMitric, Gabriel
dc.creatorVaisman, Izu
dc.date2001-08-20
dc.date.accessioned2026-07-07T04:43:02Z
dc.date.available2026-07-07T04:43:02Z
dc.descriptionThe paper starts with an interpretation of the complete lift of a Poisson structure from a manifold M to its tangent bundle TM by means of the Schouten- Nijenhuis bracket of covariant symmetric tensor fields defined by the co- tangent Lie algebroid of M. Then, we discuss Poisson structures of TM which have a graded restriction to the fiberwise polynomial algebra; they must be p-related (p is the projection of TM onto M) with a Poisson structure on M. Furthermore, we define transversal Poisson structures of a foliation, and discuss bivector fields of TM which produce graded brackets on the fiberwise polynomial algebra, and are transversal Poisson structures of the foliation by fibers. Finally, such bivector fields are produced by a process of horizontal lifting of Poisson structures from M to TM via connections.
dc.descriptionLaTex, 30 pages
dc.identifierhttps://arxiv.org/abs/math/0108130
dc.identifierhttp://arxiv.org/abs/math/0108130
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62044
dc.subjectDifferential Geometry
dc.subjectSymplectic Geometry
dc.subject53D17
dc.titlePoisson structures on tangent bundles
dc.typetext

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