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Issue 2
Mar.  2013
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ZHANG Xiao-ling. Conformal transformation between some Finsler Einstein spaces[J]. Journal of East China Normal University (Natural Sciences), 2013, (2): 160-166.
Citation: ZHANG Xiao-ling. Conformal transformation between some Finsler Einstein spaces[J]. Journal of East China Normal University (Natural Sciences), 2013, (2): 160-166.

Conformal transformation between some Finsler Einstein spaces

  • Received Date: 2012-04-01
  • Rev Recd Date: 2012-07-01
  • Publish Date: 2013-03-25
  • Liouville's Theorem proved that the Euclidean space can be mapped conformally on itself only by a composition of M\{o}bius transformations. For Riemann spaces, Brinkmann obtained general results. Little work has been done on Finsler spaces. This paper, by navigation idea and properties of conformal map, proved that the conformal transformation between Einstein Randers (or Kropina) spaces must be homothetic.
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  • [1]
    {1}

    BRINKMANN H W. Einstein spaces which are mapped conformally on each

    other[J]. Mathematische Annalen, 1925, 94(5): 119-145.
    {2}

    EINSENHART L P. Riemannian Geometry[M]. Princeton: Princenton Univ

    Press, 1926.
    {3}

    FEDISHCHENKO S I. Special conformal mappings of Riemannian spaces.

    II[J]. Ukrain Geom Sb. 1982, 25: 130-137, 144 (Russian).
    {4}

    PENROSE R, HERMANN WEYL. space-time and conformal

    geometry[C]//Hermann Weg (1885-1985). Zrich: Eidgenssische Tech

    Hochschule, 1986: 25-52.
    {5}

    K\"{U}HNEL W. Conformal transformations between Einstein

    spaces[C]//Conformal Geometry Aspects Math E 12, F. Braunschweig:

    Vieweg Sohn, 1988: 105-146.
    {6}

    K\"{U}HNEL W, RADEMACHER H B. Conformal diffeomorphisms preserving

    the Ricci tensor[J]. Proc Amer Math Soc, 1995, 123(9): 2841-2848.
    {7}

    K\"{U}HNEL W, RADEMACHER H B. Conformal transformations of

    pseudo-Riemannian manifolds[C]//Recent Developments in

    Pseudo-Riemannian Geometry. ESI Lect in Math and Phys, Z\"{u}rich:

    EMS. 2008: 261-298.
    {8}

    MIKES J, GAVRILLCHENKO M L, GLADYSHEVA, E. I. Conformal mappings

    onto Einstein spaces[J]. Mosc Univ Math Bull, 1994, 49(3): 10-14.
    {9}

    AMINOVA A V. Projective transformations of pseudo-Riemannian

    manifolds[J]. J Math Sci, 2003, 113(3): 367-470.
    {10}

    KISOSAK V A, MATVEEV V S. There are no conformal Einstein rescalings

    of complete pseudo-Riemannian Einstein metrics[J]. C R Math Acad

    Sci, 2009, 347(17-18): 1067-1069.
    {11}

    BAO D W, ROBLES C. On Ricci curvature and flag curvature in Finsler

    geometry[C]//A Sampler of Finsler Geometry: MSRI Series {\bf 50}.

    Cambriclge: Camb Univ Press, 2004: 197-259.
    {12}

    CHENG X Y, SHEN Z M, TIAN Y F. A Class of Einstein

    $(\alpha,\beta)$-metrics[J]. Israel Journal of Mathematics, 2012,

    192: 1-29.
    {13}

    ZHANG X L, SHEN Y B. On Einstein Kropina metrics[J]. Differential

    Geometry and Its Applications, 2013(31): 80-92.
    {14}

    BAO D W, CHEN X S, SHEN Z M. An Introduction to Riemann-Finsler

    Geometry[M]. Springer, 2000.
    {15}

    BAO D W, ROBLES C, SHEN Z M. Zermelo navigation on Riemannian

    manifolds[J]. Differential Geometry, 2004, 66: 377-435.
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