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Poisson structures on cotangent bundles

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  • Gabriel Mitric

Abstract

We make a study of Poisson structures of T ∗ M 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 w on the base manifold M is constructed. In particular, the horizontal lifting of a Poisson structure from M to T ∗ M 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 T ∗ M . Finally, for a 2-form ω on a Riemannian manifold, we study the conditions for some associated 2-forms of ω on T ∗ M to define Poisson structures on cotangent bundles.

Suggested Citation

  • Gabriel Mitric, 2003. "Poisson structures on cotangent bundles," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-21, January.
    • Handle: RePEc:hin:jijmms:416831
    DOI: 10.1155/S0161171203201101
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