Gabriel Mitric, "Poisson structures on cotangent bundles", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 416831, 21 pages, 2003. https://doi.org/10.1155/S0161171203201101
Poisson structures on cotangent bundles
We make a study of Poisson structures of which are graded structures when restricted to the fiberwise polynomial algebra and we give examples. A class of more general graded bivector fields which induce a given Poisson structure on the base manifold is constructed. In particular, the horizontal lifting of a Poisson structure from to via connections gives such bivector fields and we discuss the conditions for these lifts to be Poisson bivector fields and their compatibility with the canonical Poisson structure on . Finally, for a 2-form on a Riemannian manifold, we study the conditions for some associated 2-forms of on to define Poisson structures on cotangent bundles.
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