Hostname: page-component-848d4c4894-xm8r8 Total loading time: 0 Render date: 2024-07-06T22:57:35.106Z Has data issue: false hasContentIssue false
  • English
  • Français

Symplectic Lie–Rinehart–Jacobi Algebras and Contact Manifolds

Published online by Cambridge University Press:  20 November 2018

Eugène Okassa
Eugène Okassa*
Affiliation:
Université Marien NGOUABI, Faculté des Sciences, Département de Mathematiques, B.P. 69 Brazzaville, Congoe-mail: eugeneokassa@yahoo.fr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give a characterization of contact manifolds in terms of symplectic Lie–Rinehart–Jacobi algebras. We also give a sufficient condition for a Jacobi manifold to be a contact manifold.

Keywords

13N0553D0553D10Lie–Rinehart algebrasdifferential operatorsJacobi manifoldssymplectic manifoldscontact manifolds
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 4 , 01 December 2011 , pp. 716 - 725
Copyright
Copyright © Canadian Mathematical Society 2011

References

[1] Godbillon, C., Géométrie différentielle et mécanique analytique. Hermann, Paris, 1969.Google Scholar
[2] Lichnerowicz, A., Les variétés de Jacobi et leurs algèbres de Lie associées. J. Math. Pures Appl. 57(1978), no. 4, 453–488.Google Scholar
[3] Okassa, E., Algèbres de Jacobi et Algèbres de Lie–Rinehart–Jacobi. J. Pure Appl. Algebra 208(2007), no. 3, 1071–1089. doi:10.1016/j.jpaa.2006.05.013Google Scholar
[4] Okassa, E., On Lie–Rinehart–Jacobi algebras. J. Algebra Appl. 7(2008), no. 6, 749–772. doi:10.1142/S0219498808003107Google Scholar
[5] Rinehart, G., Differential forms for general commutative algebras.. Trans. Amer. Math. Soc. 108(1963), 195–222. doi:10.1090/S0002-9947-1963-0154906-3Google Scholar