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On a class of locally dually flat (α,β)-metrics

Funds:  Supported by the NSF of Chizhou University (2014ZRZ011).
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https://doi.org/10.3969/j.issn.0253-2778.2018.11.003
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  • Corresponding author: HUA Yiping (corresponding author), female, born in 1982, master/lecturer. Research field: Differential geometry. E-mail: huayiping@yeah.net
  • Received Date: 24 June 2017
  • Accepted Date: 22 July 2017
  • Rev Recd Date: 22 July 2017
  • Publish Date: 30 November 2018
    Abstract

  • Abstract

    Locally dually flat weak Landsberg(α,β)-metrics in the form of F=α(βα) were studied,

    Abstract

    Locally dually flat weak Landsberg(α,β)-metrics in the form of F=α(βα) were studied,
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    • References(9)
  • [1]
    SHEN Z. Riemann-Finsler geometry with application to information geometry[J]. Chin Ann Math, 2006, 27(1): 73-94.
    [2]
    CHENG X, SHEN Z, ZHOU Y. On locally dually flat Finsler metrics[J]. International Journal of Mathematics, 2010, 21(11): 1531-1543.
    [3]
    XIA Q. On locally dually flat (α，β)-metrics[J]. Differential Geometry and Its Application, 2011, 29(2): 233-243.
    [4]
    ZOU Y, CHENG X. The generalized unicorn problem on (α，β)-metric[J]. J Math Anal Appl, 2014, 414: 574-589.
    [5]
    CHERN S S, SHEN Z. Riemannian-Finsler Geometry[M]. Singapore：World Scientific Publisher, 2005.
    [6]
    LI B, SHEN Z. On a class of weak Landsberg metrics[J]. Science in China Series A, 2007, 50: 75-85.
    [7]
    CHENG X, LI H, ZOU Y. On conformally flat (α，β)-metrics with relatively isotropic mean Landsberg curvature[J]. Publ Math Debrecen, 2014, 85: 131-144.
    [8]
    CHENG X, ZOU Y. The generalized unicorn problem in Finsler geometry[J]. Differ Geom Dyn syst, 2015, 17: 38-48.
    [9]
    CHENG X, SHEN Z. Randers metrics with special curvature properties[J]. Osaka J Math, 2003, 40: 87-101.)
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    [1]
    SHEN Z. Riemann-Finsler geometry with application to information geometry[J]. Chin Ann Math, 2006, 27(1): 73-94.
    [2]
    CHENG X, SHEN Z, ZHOU Y. On locally dually flat Finsler metrics[J]. International Journal of Mathematics, 2010, 21(11): 1531-1543.
    [3]
    XIA Q. On locally dually flat (α，β)-metrics[J]. Differential Geometry and Its Application, 2011, 29(2): 233-243.
    [4]
    ZOU Y, CHENG X. The generalized unicorn problem on (α，β)-metric[J]. J Math Anal Appl, 2014, 414: 574-589.
    [5]
    CHERN S S, SHEN Z. Riemannian-Finsler Geometry[M]. Singapore：World Scientific Publisher, 2005.
    [6]
    LI B, SHEN Z. On a class of weak Landsberg metrics[J]. Science in China Series A, 2007, 50: 75-85.
    [7]
    CHENG X, LI H, ZOU Y. On conformally flat (α，β)-metrics with relatively isotropic mean Landsberg curvature[J]. Publ Math Debrecen, 2014, 85: 131-144.
    [8]
    CHENG X, ZOU Y. The generalized unicorn problem in Finsler geometry[J]. Differ Geom Dyn syst, 2015, 17: 38-48.
    [9]
    CHENG X, SHEN Z. Randers metrics with special curvature properties[J]. Osaka J Math, 2003, 40: 87-101.)
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