Warped Poisson brackets on warped products

Yacine Aït Amrane; Rafik Nasri; Ahmed Zeglaoui

doi:10.3934/jgm.2014.6.279

Article Contents

2014, Volume 6, Issue 3: 279-296. Doi: 10.3934/jgm.2014.6.279

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Warped Poisson brackets on warped products

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

Received: January 2013

Revised: August 2014

Published: September 2014

Abstract / Introduction Related Papers Cited by

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.

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Mathematics Subject Classification: 53C15, 53D17.

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References

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