International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 29, Pages 1833-1853
doi:10.1155/S0161171203201101
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.