Poisson structures on cotangent bundles

Gabriel Mitric

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-21

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.

Date: 2003
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2003/416831.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2003/416831.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:416831

DOI: 10.1155/S0161171203201101

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().