International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 29, Pages 1833-1853

Poisson structures on cotangent bundles

Gabriel Mitric

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.


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.