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A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold
Репозиторій DSpace/Manakin
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold
Інший ID:
2000 Mathematics Subject Classification: 37J35; 53C60; 70H06
Посилання:
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.
Підтримка:
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).
Дата:
2007
Переглядів:
604
Завантажень:
271
Анотація:
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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