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• W2513591707 abstract "The 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 cotangent Lie algebroid of M. Then, we discuss Poisson structures of TM which have a graded restriction to the fiberwise polynomial algebra; they must be π-related (π:TM→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." @default.
• W2513591707 created "2016-09-16" @default.
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• W2513591707 date "2003-03-01" @default.
• W2513591707 modified "2023-09-27" @default.
• W2513591707 title "Poisson structures on tangent bundles" @default.
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• W2513591707 doi "https://doi.org/10.1016/s0926-2245(02)00148-1" @default.
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