International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 29, Pages 1833-1853
doi:10.1155/S0161171203201101
Poisson structures on cotangent bundles
Catedra de Geometrie, Universitatea “Alexandru Ioan Cuza”, Iaşi 6600, Romania
Received 22 January 2002
Copyright © 2003 Gabriel Mitric. 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.
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.