|XXXIV Workshop on Geometric Methods in Physics||28.06-4.07.2015|
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warped Poisson brackets on warped products
In this work, we generalize the geometry of the product pseudo-riemannian manifold equipped with the Poisson structure to the geometry of warped product of pseudo-riemannian manifold equipped with a warped Poisson structure. We construct three bivector fields on a product manifold and we show that each of them under certain condition to a Poisson structure. One of these bivector fields will be called warped bivector field. For a warped product of pseudo-riemannian manifolds equipped with a warped bivector field, we compute the correspending contravariant Levi-Civita connexion and the curvatures associated with.