Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2017 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148578 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862707977238085632 |
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| author | Işim Efe, M. Abadoğlu, E. |
| author_facet | Işim Efe, M. Abadoğlu, E. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T17:08:37Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148578 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:08:37Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Işim Efe, M. Abadoğlu, E. 2019-02-18T16:11:46Z 2019-02-18T16:11:46Z 2017 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. 1815-0659 2010 Mathematics Subject Classification: 53D17; 53D35 DOI:10.3842/SIGMA.2017.055 https://nasplib.isofts.kiev.ua/handle/123456789/148578 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds Article published earlier |
| spellingShingle | Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds Işim Efe, M. Abadoğlu, E. |
| title | Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds |
| title_full | Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds |
| title_fullStr | Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds |
| title_full_unstemmed | Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds |
| title_short | Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds |
| title_sort | global existence of bi-hamiltonian structures on orientable three-dimensional manifolds |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148578 |
| work_keys_str_mv | AT isimefem globalexistenceofbihamiltonianstructuresonorientablethreedimensionalmanifolds AT abadoglue globalexistenceofbihamiltonianstructuresonorientablethreedimensionalmanifolds |