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arXiv · 2305.18595

Global Compatibility of Bi-Hamiltonian Structures on Three Dimensional Manifolds

Beste Madran·Ender Abadoğlu
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Abstract

It is shown in \cite{yazar6} that a 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, and the bi-Hamiltonian structure is globally compatible if and only if the Bott class of the complex codimension one foliation defined by the nonvanishing vector field vanishes. In this work, we constructed a dynamical system on $S^3$, which is globally bi-Hamiltonian, but the Hamiltonians are not globally compatible.

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Beste Madran, Ender Abadoğlu. 2023-05-29. Global Compatibility of Bi-Hamiltonian Structures on Three Dimensional Manifolds. https://arxiv.org/abs/2305.18595

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