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The Journal of Geometric Mechanics (JGM)
 

Warped Poisson brackets on warped products

Pages: 279 - 296, Volume 6, Issue 3, September 2014      doi:10.3934/jgm.2014.6.279

 
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Yacine Aït Amrane - Laboratory of Algebra and Number Theory, Faculté de Mathématiques, USTHB, BP32, El-Alia, 16111 Bab-Ezzouar, Alger, Algeria (email)
Rafik Nasri - Laboratory of Geometry, Analysis, Control and Applications, Université de Saïda, BP138, En-Nasr, 20000 Saïda, Algeria (email)
Ahmed Zeglaoui - Laboratory of Algebra and Number Theory, Faculté de Mathématiques, USTHB, BP32, El-Alia, 16111 Bab-Ezzouar, Alger, Algeria (email)

Abstract: In this paper, we generalize the geometry of the product pseudo-Riemannian manifold equipped with the product Poisson structure ([10]) to the geometry of a warped product of pseudo-Riemannian manifolds equipped with a warped Poisson structure. We construct three bivector fields on a product manifold and show that each of them lead under certain conditions to a Poisson structure. One of these bivector fields will be called the warped bivector field. For a warped product of pseudo-Riemannian manifolds equipped with a warped bivector field, we compute the corresponding contravariant Levi-Civita connection and the curvatures associated with.

Keywords:  Warped products, warped Poisson brackets, generalized Poisson brackets, metacurvature, pseudo-Riemannian Poisson manifolds, Levi-Civita contravariant connections.
Mathematics Subject Classification:  53C15, 53D17.

Received: January 2013;      Revised: August 2014;      Available Online: September 2014.

 References