Integrable Flows for Starlike Curves in Centroaffine Space
We construct integrable hierarchies of flows for curves in centroaffine R³ through a natural pre-symplectic structure on the space of closed unparametrized starlike curves. We show that the induced evolution equations for the differential invariants are closely connected with the Boussinesq hierarch...
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| Дата: | 2013 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2013
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149224 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Integrable Flows for Starlike Curves in Centroaffine Space / A. Calini, T. Ivey, G.M. Beffa // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 30 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1492242019-02-20T01:26:45Z Integrable Flows for Starlike Curves in Centroaffine Space Calini, A. Ivey, T. Beffa, G.M. We construct integrable hierarchies of flows for curves in centroaffine R³ through a natural pre-symplectic structure on the space of closed unparametrized starlike curves. We show that the induced evolution equations for the differential invariants are closely connected with the Boussinesq hierarchy, and prove that the restricted hierarchy of flows on curves that project to conics in RP² induces the Kaup-Kuperschmidt hierarchy at the curvature level. 2013 Article Integrable Flows for Starlike Curves in Centroaffine Space / A. Calini, T. Ivey, G.M. Beffa // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 30 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K10; 53A20; 53C44 DOI: http://dx.doi.org/10.3842/SIGMA.2013.022 http://dspace.nbuv.gov.ua/handle/123456789/149224 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 |
We construct integrable hierarchies of flows for curves in centroaffine R³ through a natural pre-symplectic structure on the space of closed unparametrized starlike curves. We show that the induced evolution equations for the differential invariants are closely connected with the Boussinesq hierarchy, and prove that the restricted hierarchy of flows on curves that project to conics in RP² induces the Kaup-Kuperschmidt hierarchy at the curvature level. |
| format |
Article |
| author |
Calini, A. Ivey, T. Beffa, G.M. |
| spellingShingle |
Calini, A. Ivey, T. Beffa, G.M. Integrable Flows for Starlike Curves in Centroaffine Space Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Calini, A. Ivey, T. Beffa, G.M. |
| author_sort |
Calini, A. |
| title |
Integrable Flows for Starlike Curves in Centroaffine Space |
| title_short |
Integrable Flows for Starlike Curves in Centroaffine Space |
| title_full |
Integrable Flows for Starlike Curves in Centroaffine Space |
| title_fullStr |
Integrable Flows for Starlike Curves in Centroaffine Space |
| title_full_unstemmed |
Integrable Flows for Starlike Curves in Centroaffine Space |
| title_sort |
integrable flows for starlike curves in centroaffine space |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149224 |
| citation_txt |
Integrable Flows for Starlike Curves in Centroaffine Space / A. Calini, T. Ivey, G.M. Beffa // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 30 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT calinia integrableflowsforstarlikecurvesincentroaffinespace AT iveyt integrableflowsforstarlikecurvesincentroaffinespace AT beffagm integrableflowsforstarlikecurvesincentroaffinespace |
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2023-05-20T17:32:16Z |
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2023-05-20T17:32:16Z |
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