Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds
Symplectic Geometry
2017-07-17 v2
Abstract
In this work, we show that an autonomous dynamical system defined by a nonvanishing vector field on an orientable three-dimensional manifold is globally bi-Hamiltonian if and only if the first Chern class of the normal bundle of the given vector field vanishes. Furthermore, the bi-Hamiltonian structure is globally compatible if and only if the Bott class of the complex codimension one foliation defined by the given vector field vanishes.
Keywords
Cite
@article{arxiv.1612.06996,
title = {Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds},
author = {Melike Işim Efe and Ender Abadoğlu},
journal= {arXiv preprint arXiv:1612.06996},
year = {2017}
}