Regular Foliations and Poisson Structures on Orientable Manifolds

Rubén Flores-Espinoza; Misael Avendaño-Camacho

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arXiv · 1512.05040

Regular Foliations and Poisson Structures on Orientable Manifolds

Rubén Flores-Espinoza·Misael Avendaño-Camacho

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Abstract

On an orientable manifold M, we consider a regular even dimensional foliation F which is globally defined by a set of k-independent 1-forms. We give necessary and sufficient conditions for the existence of a regular Poisson structure on M whose Characteristic foliation is precisely F. Moreover, introducing a special class of the foliated 1-cohomology we describe obstructions for the existence of unimodular Poisson structures with a given characteristic foliation. In the same lines, we also give conditions for the existence of transversally constant Poisson structures.

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Rubén Flores-Espinoza, Misael Avendaño-Camacho. 2015-12-16. Regular Foliations and Poisson Structures on Orientable Manifolds. https://arxiv.org/abs/1512.05040

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