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arXiv · 1804.05946

Compatible Poisson Structures on Fibered $5$-Manifolds

R. Flores-Espinoza·J. C. Ruíz-Pantaleón·Yu. Vorobiev
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Abstract

We study a class of Poisson tensors on a fibered manifold which are compatible with the fiber bundle structure by the so-called almost coupling condition. In the case of a $5$-dimensional orientable fibered manifolds with $2$-dimensional bases, we describe a global behavior of almost coupling Poisson tensors and their singularities by using a bigraded factorization of the Jacobi identity. In particular, we present some unimodularity criteria and describe a class of gauge type transformations preserving the almost coupling property.

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R. Flores-Espinoza, J. C. Ruíz-Pantaleón, Yu. Vorobiev. 2018-04-16. Compatible Poisson Structures on Fibered $5$-Manifolds. https://doi.org/10.1007/s40590-018-0225-7

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