Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds

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.

References in corpus (2)

• New solutions of the Jacobi equations for three-dimensional Poisson structures
• On the Relationship between Two Notions of Compatibility for Bi-Hamiltonian Systems

Cited by in corpus (1)

• Sasakian structure associated with a second order ODE and Hamiltonian dynamical systems