Poisson structures on cotangent bundles
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 horizon...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203201101 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |