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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832563895338795008 |
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| author | Gabriel Mitric |
| author_facet | Gabriel Mitric |
| author_sort | Gabriel Mitric |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2cbd2765f090414f9618539ef701cb23 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-2cbd2765f090414f9618539ef701cb232025-02-03T01:12:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003291833185310.1155/S0161171203201101Poisson structures on cotangent bundlesGabriel Mitric0Catedra de Geometrie, Universitatea “Alexandru Ioan Cuza”, Iaşi 6600, RomaniaWe 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.http://dx.doi.org/10.1155/S0161171203201101 |
| spellingShingle | Gabriel Mitric Poisson structures on cotangent bundles International Journal of Mathematics and Mathematical Sciences |
| title | Poisson structures on cotangent bundles |
| title_full | Poisson structures on cotangent bundles |
| title_fullStr | Poisson structures on cotangent bundles |
| title_full_unstemmed | Poisson structures on cotangent bundles |
| title_short | Poisson structures on cotangent bundles |
| title_sort | poisson structures on cotangent bundles |
| url | http://dx.doi.org/10.1155/S0161171203201101 |
| work_keys_str_mv | AT gabrielmitric poissonstructuresoncotangentbundles |