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arXiv · 1308.6123

Warped Poisson Brackets on Warped Products

Yacine Aït Amrane·Rafik Nasri·Ahmed Zeglaoui
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Abstract

In this paper, we generalize the geometry of the product pseudo-Riemannian manifold equipped with the product Poisson structure (\cite{Nas2}) 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.

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Yacine Aït Amrane, Rafik Nasri, Ahmed Zeglaoui. 2013-08-28. Warped Poisson Brackets on Warped Products. https://doi.org/10.3934/jgm.2014.6.279

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