A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold
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| Creator |
Sarlet, W.
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| 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 |
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| Date |
2019-02-16T08:14:44Z
2019-02-16T08:14:44Z 2007 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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