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Poisson Vector Fields on Weil Bundles
Faculty of Sciences and Technology, Marien NGOUABI University, Brazzaville, Congo
Institut de Recherche en Sciences Exactes et Naturelles (IRSEN), Brazzaville, Congo
- 1 Faculty of Sciences and Technology, Marien NGOUABI University, Brazzaville, Congo
- 2 Institut de Recherche en Sciences Exactes et Naturelles (IRSEN), Brazzaville, Congo
Advances in Pure Mathematics·Volume 05 (2015)·Pages 757–766·Published 9 November 2015·DOI10.4236/apm.2015.513069
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Abstract
In this paper, M is a smooth manifold of finite dimension n, A is a local algebra and M A is the associated Weil bundle. We study Poisson vector fields on M A and we prove that all globally hamiltonian vector fields on M A are Poisson vector fields.
KeywordsWeil AlgebraWeil BundlePoisson ManifoldLie DerivativePoisson 2-Form
- Weil, A. (1953) Théorie des points proches sur les variétés différentiables. Colloq. Géom. Diff. Strasbourg, 111-117.
- Morimoto, A. (1976) Prolongation of Connections to Bundles of Infinitely Near Points. Journal of Differential Geometry, 11, 479-498.
- Okassa, E. (1986-1987) Prolongement des champs de vecteurs à des variétés des points prohes. Annales de la Faculté des Sciences de Toulouse, 3, 346-366.
- Bossoto, B.G.R. and Okassa, E. (2008) Champs de vecteurs et formes différentielles sur une variété des points proches. Archivum Mathematicum, Tomus, 44, 159-171.
- Kolár, P., Michor, P.W. and Slovak, J. (1993) Natural Operations in Differential Geometry. Springer-Verlag, Berlin. http://dx.doi.org/10.1007/978-3-662-02950-3
- Moukala Mahoungou, N. and Bossoto, B.G.R. (2015) Hamiltonian Vector Fields on Weil Bundles. Journal of Mathematics Research, 7, 141-148. http://dx.doi.org/10.5539/jmr.v7n3p141
- Laurent-Gengoux, C., Pichereau, A. and Vanhaecke, P. (2013) Poisson Structures. Grundlehren der mathematischen Wissenschaften, 347. www.springer.com/series/138
- Okassa, E. (2007) Algèbres de Jacobi et Algèbres de Lie-Rinehart-Jacobi. Journal of Pure and Applied Algebra, 208, 1071-1089. http://dx.doi.org/10.1016/j.jpaa.2006.05.013
- Moukala Mahoungou, N. and Bossoto, B. G.R. Prolongation of Poisson 2-Form on Weil Bundles.
- Lichnerowicz, A. (1977) Les variétés de Poisson et leurs algèbres de Lie associées. Journal of Differential Geometry, 12, 253-300.
- Vaisman, I. (1994) Lectures on the Geometry of Poisson Manifolds. Progress in Mathematics 118, Birkhäuser Verlag, Basel. http://dx.doi.org/10.1007/978-3-0348-8495-2
- Bossoto, B.G.R. and Okassa, E. (2012) A-Poisson Structures on Weil Bundles. International Journal of Contemporary Mathematical Sciences, 7, 785-803.
- Nkou, V.B., Bossoto, B.G.R. and Okassa, E. (2015) New Characterization of Vector Field on Weil Bundles. Theoretical Mathematics and Applications, 5, 1-17.