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Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds
Інший ID:
2010 Mathematics Subject Classification: 53D17; 53D35
DOI:10.3842/SIGMA.2017.055
DOI:10.3842/SIGMA.2017.055
Посилання:
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.
Підтримка:
We are indebted to Professor Turgut Onder for his help during this work. We also thank to the ¨
anonymous referees for their comments and corrections.
Дата:
2017
Переглядів:
796
Завантажень:
276
Анотація:
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.
