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A recursive scheme of first integrals of the geodesic flow of a Finsler manifold

Willy Sarlet (UGent)
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Abstract
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 tau : 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.
Keywords
special conformal Killing tensors, Finsler spaces

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Citation

Please use this url to cite or link to this publication:

MLA
Sarlet, Willy. “A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold.” SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS 3 (2007): n. pag. Print.
APA
Sarlet, Willy. (2007). A recursive scheme of first integrals of the geodesic flow of a Finsler manifold. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 3.
Chicago author-date
Sarlet, Willy. 2007. “A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold.” Symmetry Integrability and Geometry-methods and Applications 3.
Chicago author-date (all authors)
Sarlet, Willy. 2007. “A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold.” Symmetry Integrability and Geometry-methods and Applications 3.
Vancouver
1.
Sarlet W. A recursive scheme of first integrals of the geodesic flow of a Finsler manifold. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS. 2007;3.
IEEE
[1]
W. Sarlet, “A recursive scheme of first integrals of the geodesic flow of a Finsler manifold,” SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, vol. 3, 2007.
@article{392754,
  abstract     = {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 tau : 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.},
  articleno    = {024},
  author       = {Sarlet, Willy},
  issn         = {1815-0659},
  journal      = {SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS},
  keywords     = {special conformal Killing tensors,Finsler spaces},
  language     = {eng},
  pages        = {9},
  title        = {A recursive scheme of first integrals of the geodesic flow of a Finsler manifold},
  url          = {http://www.emis.de/journals/SIGMA/2007/024/},
  volume       = {3},
  year         = {2007},
}

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