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...
Збережено в:
| Дата: | 2007 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2007
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147793 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| 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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147793 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1477932019-02-17T01:27:26Z A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold Sarlet, W. 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 2007 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147793 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 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 |
| format |
Article |
| author |
Sarlet, W. |
| spellingShingle |
Sarlet, W. A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Sarlet, W. |
| author_sort |
Sarlet, W. |
| title |
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_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_sort |
recursive scheme of first integrals of the geodesic flow of a finsler manifold |
| publisher |
Інститут математики НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147793 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT sarletw arecursiveschemeoffirstintegralsofthegeodesicflowofafinslermanifold AT sarletw recursiveschemeoffirstintegralsofthegeodesicflowofafinslermanifold |
| first_indexed |
2023-05-20T17:28:32Z |
| last_indexed |
2023-05-20T17:28:32Z |
| _version_ |
1796153384138440704 |