{
  "id": "math/0702383",
  "version": "v1",
  "published": "2007-02-13T17:30:10.000Z",
  "updated": "2007-02-13T17:30:10.000Z",
  "title": "A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold",
  "authors": [
    "Willy Sarlet"
  ],
  "comment": "This is a contribution to the Proc. of workshop on Geometric Aspects of Integrable Systems (July 17-19, 2006; Coimbra, Portugal), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/",
  "journal": "SIGMA 3 (2007), 024, 9 pages",
  "doi": "10.3842/SIGMA.2007.024",
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "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 $\\tau: TQ\\to Q$ 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-02-13T17:30:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first integrals",
      "recursive scheme",
      "geodesic flow",
      "finsler manifold",
      "special conformal killing tensors"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "SIGMA",
      "year": 2007,
      "month": "Feb",
      "volume": 3,
      "pages": "024"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007SIGMA...3..024S"
    }
  }
}