Prolongation of Poisson 2 -form on Weil bundles

Norbert Mahoungou Moukala; Basile Guy Richard Bossoto

Archivum Mathematicum (2016)

  • Volume: 052, Issue: 2, page 91-111
  • ISSN: 0044-8753

Abstract

top
In this paper, M denotes a smooth manifold of dimension n , A a Weil algebra and M A the associated Weil bundle. When ( M , ω M ) is a Poisson manifold with 2 -form ω M , we construct the 2 -Poisson form ω M A A , prolongation on M A of the 2 -Poisson form ω M . We give a necessary and sufficient condition for that M A be an A -Poisson manifold.

How to cite

top

Moukala, Norbert Mahoungou, and Bossoto, Basile Guy Richard. "Prolongation of Poisson $2$-form on Weil bundles." Archivum Mathematicum 052.2 (2016): 91-111. <http://eudml.org/doc/281536>.

@article{Moukala2016,
abstract = {In this paper, $M$ denotes a smooth manifold of dimension $n$, $A$ a Weil algebra and $M^\{A\}$ the associated Weil bundle. When $(M,\omega _\{M\})$ is a Poisson manifold with $2$-form $\omega _\{M\}$, we construct the $2$-Poisson form $\omega _\{M^\{A\}\}^\{A\}$, prolongation on $M^\{A\}$ of the $2$-Poisson form $\omega _\{M\}$. We give a necessary and sufficient condition for that $M^\{A\}$ be an $A$-Poisson manifold.},
author = {Moukala, Norbert Mahoungou, Bossoto, Basile Guy Richard},
journal = {Archivum Mathematicum},
keywords = {Weil bundle; Weil algebra; Poisson manifold; Lie derivative; Poisson 2-form},
language = {eng},
number = {2},
pages = {91-111},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Prolongation of Poisson $2$-form on Weil bundles},
url = {http://eudml.org/doc/281536},
volume = {052},
year = {2016},
}

TY - JOUR
AU - Moukala, Norbert Mahoungou
AU - Bossoto, Basile Guy Richard
TI - Prolongation of Poisson $2$-form on Weil bundles
JO - Archivum Mathematicum
PY - 2016
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 052
IS - 2
SP - 91
EP - 111
AB - In this paper, $M$ denotes a smooth manifold of dimension $n$, $A$ a Weil algebra and $M^{A}$ the associated Weil bundle. When $(M,\omega _{M})$ is a Poisson manifold with $2$-form $\omega _{M}$, we construct the $2$-Poisson form $\omega _{M^{A}}^{A}$, prolongation on $M^{A}$ of the $2$-Poisson form $\omega _{M}$. We give a necessary and sufficient condition for that $M^{A}$ be an $A$-Poisson manifold.
LA - eng
KW - Weil bundle; Weil algebra; Poisson manifold; Lie derivative; Poisson 2-form
UR - http://eudml.org/doc/281536
ER -

References

top
  1. Bossoto, B.G.R., Okassa, E., Champs de vecteurs et formes différentielles sur une variété des points proches, Arch. Math. (Brno) 44 (2008), 159–171. (2008) Zbl1212.13016MR2432853
  2. Bossoto, B.G.R., Okassa, E., A-poisson structures on Weil bundles, Int. J. Contemp. Math. Sci. 7 (16) (2012), 785–803. (2012) Zbl1247.53093MR2901677
  3. Kolář, I., Michor, P.W., Slovák, J., Natural Operations in Differential Geometry, Springer, Berlin, 1993. (1993) MR1202431
  4. Laurent-Gengoux, C., Pichereau, A., Vanhaecke, P., Poisson Structures, Grundlehren Math. Wiss. 347 (2013), www.springer.com/series/138. (2013) MR2906391
  5. Lichnerowicz, A., 10.4310/jdg/1214433987, J. Differential Geom. 12 (1977), 253–300. (1977) Zbl0405.53024MR0501133DOI10.4310/jdg/1214433987
  6. Morimoto, A., 10.4310/jdg/1214433720, J. Differential Geom. 11 (1976), 479–498. (1976) Zbl0358.53013MR0445422DOI10.4310/jdg/1214433720
  7. Moukala, N.M., Bossoto, B.G.R., 10.5539/jmr.v7n3p141, Journal of Mathematics Research 7 (3) (2015), 141–148. (2015) DOI10.5539/jmr.v7n3p141
  8. Nkou, V.B., Bossoto, B.G.R., Okassa, E., New characterization of vector field on Weil bundles, Theoretical Mathematics Applications 5 (2) (2015), 1–17, arXiv:1504.04483 [math.DG]. (2015) 
  9. Okassa, E., Prolongement des champs de vecteurs à des variétés des points proches, Ann. Fac. Sci. Toulouse Math. (5) 8 (3) (1986–1987), 346–366. (1986) MR0948759
  10. Okassa, E., 10.1016/j.jpaa.2006.05.013, J. Pure Appl. Algebra 208 (3) (2007), 1071–1089. (2007) Zbl1163.17025MR2283447DOI10.1016/j.jpaa.2006.05.013
  11. Okassa, E., 10.1142/S0219498808003107, J. Algebra Appl. 7 (2008), 749–772. (2008) Zbl1226.17017MR2483330DOI10.1142/S0219498808003107
  12. Okassa, E., 10.4153/CMB-2011-033-6, Canad. Math. Bull. 54 (4) (2011), 716–725. (2011) Zbl1232.53062MR2894521DOI10.4153/CMB-2011-033-6
  13. Shurygin, V.V., 10.1007/s10958-010-0051-6, J. Math. Sci. (New York) 169 (3) (2010), 315–341. (2010) MR2866746DOI10.1007/s10958-010-0051-6
  14. Vaisman, I., Lectures on the Geometry of Poisson Manifolds, Progress in Math., vol. 118, Birkhäuser Verlag, Basel, 1994. (1994) Zbl0810.53019MR1269545
  15. Weil, A., Théorie des points proches sur les variétés différentiables, Colloques Internationaux du Centre National de la Recherche Scientifique, Strasbourg (1953), 111–117. (1953) Zbl0053.24903MR0061455

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.