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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2017
• Main Authors: Işim Efe, M., Abadoğlu, E.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2017
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148578
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds / M. Işim Efe, E. Abadoğlu // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 13 назв. — англ.

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 struct...