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...
Збережено в:
| Дата: | 2017 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2017
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148578 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-148578 |
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dspace |
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irk-123456789-1485782019-02-19T01:31:29Z Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds Işim Efe, M. Abadoğlu, E. 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. 2017 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/148578 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Işim Efe, M. Abadoğlu, E. |
| spellingShingle |
Işim Efe, M. Abadoğlu, E. Global Existence of Bi-Hamiltonian Structures on Orientable Three-Dimensional Manifolds Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Işim Efe, M. Abadoğlu, E. |
| author_sort |
Işim Efe, M. |
| title |
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_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_sort |
global existence of bi-hamiltonian structures on orientable three-dimensional manifolds |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148578 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT isimefem globalexistenceofbihamiltonianstructuresonorientablethreedimensionalmanifolds AT abadoglue globalexistenceofbihamiltonianstructuresonorientablethreedimensionalmanifolds |
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2023-05-20T17:30:52Z |
| last_indexed |
2023-05-20T17:30:52Z |
| _version_ |
1796153470135304192 |