A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold
We review properties of so-called special conformal Killing tensors on a Riemannian manifold (Q,g) and the way they give rise to a Poisson-Nijenhuis structure on the tangent bundle TQ. We then address the question of generalizing this concept to a Finsler space, where the metric tensor field comes f...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2007 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2007
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147793 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold / W. Sarlet // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 6 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862751258290421760 |
|---|---|
| author | Sarlet, W. |
| author_facet | Sarlet, W. |
| citation_txt | A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold / W. Sarlet // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 6 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We review properties of so-called special conformal Killing tensors on a Riemannian manifold (Q,g) and the way they give rise to a Poisson-Nijenhuis structure on the tangent bundle TQ. We then address the question of generalizing this concept to a Finsler space, where the metric tensor field comes from a regular Lagrangian function E, homogeneous of degree two in the fibre coordinates on TQ. It is shown that when a symmetric type (1,1) tensor field K along the tangent bundle projection τ: TQ→ Q satisfies a differential condition which is similar to the defining relation of special conformal Killing tensors, there exists a direct recursive scheme again for first integrals of the geodesic spray. Involutivity of such integrals, unfortunately, remains an open problem. 
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| first_indexed | 2025-12-07T21:10:15Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147793 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:10:15Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Sarlet, W. 2019-02-16T08:14:44Z 2019-02-16T08:14:44Z 2007 A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold / W. Sarlet // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 6 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 37J35; 53C60; 70H06 https://nasplib.isofts.kiev.ua/handle/123456789/147793 We review properties of so-called special conformal Killing tensors on a Riemannian manifold (Q,g) and the way they give rise to a Poisson-Nijenhuis structure on the tangent bundle TQ. We then address the question of generalizing this concept to a Finsler space, where the metric tensor field comes from a regular Lagrangian function E, homogeneous of degree two in the fibre coordinates on TQ. It is shown that when a symmetric type (1,1) tensor field K along the tangent bundle projection τ: TQ→ Q satisfies a differential condition which is similar to the defining relation of special conformal Killing tensors, there exists a direct recursive scheme again for first integrals of the geodesic spray. Involutivity of such integrals, unfortunately, remains an open problem. 
 Remove selected This paper is a contribution to the Proceedings of the Workshop on Geometric Aspects of Integrable Systems (July 17–19, 2006, University of Coimbra, Portugal). This work has been partially supported by the European Union through the FP6 Marie Curie RTN ENIGMA (Contract number MRTN-CT-2004-5652). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold Article published earlier |
| spellingShingle | A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold Sarlet, W. |
| title | A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold |
| title_full | A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold |
| title_fullStr | A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold |
| title_full_unstemmed | A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold |
| title_short | A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold |
| title_sort | recursive scheme of first integrals of the geodesic flow of a finsler manifold |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147793 |
| work_keys_str_mv | AT sarletw arecursiveschemeoffirstintegralsofthegeodesicflowofafinslermanifold AT sarletw recursiveschemeoffirstintegralsofthegeodesicflowofafinslermanifold |