# American Institute of Mathematical Sciences

September  2014, 6(3): 279-296. doi: 10.3934/jgm.2014.6.279

## Warped Poisson brackets on warped products

 1 Laboratory of Algebra and Number Theory, Faculté de Mathématiques, USTHB, BP32, El-Alia, 16111 Bab-Ezzouar, Alger, Algeria, Algeria 2 Laboratory of Geometry, Analysis, Control and Applications, Université de Saïda, BP138, En-Nasr, 20000 Saïda, Algeria

Received  January 2013 Revised  August 2014 Published  September 2014

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.
Citation: Yacine Aït Amrane, Rafik Nasri, Ahmed Zeglaoui. Warped Poisson brackets on warped products. Journal of Geometric Mechanics, 2014, 6 (3) : 279-296. doi: 10.3934/jgm.2014.6.279
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