International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 416831 | https://doi.org/10.1155/S0161171203201101

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

Received22 Jan 2002

Abstract

We make a study of Poisson structures of TM 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 TM 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 TM. Finally, for a 2-form ω on a Riemannian manifold, we study the conditions for some associated 2-forms of ω on TM to define Poisson structures on cotangent bundles.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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