arXiv subjects

Rubén Flores-Espinoza

Publications and source records attributed to Rubén Flores-Espinoza.

2 recordsLinked to original sources

arXiv2015

On Poisson structures on R4

This paper is devoted to the study of Poisson structures on the Euclidean four dimensional space R4. By using the properties of the trace operator associated to a volumen form and the elementary vector calculus operations in R3, we give explicit formulas for the main geometric objects associated to the Poisson structures in R4, including its characteristic foliation, the Hamiltonian and Poisson vector fields, normal forms and some useful decomposition formulae for Poisson tensors. We also discuss the class of unimodular Poisson structures and give two results about the existence of Poisson structures having as its characteristic foliation a given arbitrary regular foliation.

math-ph↗

arXiv2015

Regular Foliations and Poisson Structures on Orientable Manifolds

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.

math.DG↗