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On general $(\alpha,\beta)$-metrics with isotropic $E$-curvature

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General $(\alpha,\beta)$-metrics form a rich and important class of Finsler metrics. In this paper, we obtain a differential equation which characterizes a general $(\alpha,\beta)$-metric with isotropic $E$-curvature, under a certain condition. We also solve the equation in a particular case.

Abstract

General $(\alpha,\beta)$-metrics form a rich and important class of Finsler metrics. In this paper, we obtain a differential equation which characterizes a general $(\alpha,\beta)$-metric with isotropic $E$-curvature, under a certain condition. We also solve the equation in a particular case.

참고문헌 (13)

  1. X. Chen, "On Douglas metrics", Publ. Math. Debrecen, 66(3-4), pp.503~512 (2005)
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  3. S.-S. Chern, "Finsler geometry is just Riemannian geometry without the quadratic restriction", Notices Amer. Math. Soc., 43(9), pp.959~963 (1996)
  4. B. Li, "Projectively flat fourth root Finsler metrics", Canad. Math. Bull., 55(1), pp.138~145 (2012)[DOI]
  5. S. F. Rutz, "Symmetry in Finsler spaces, Contemp. Math., 196", pp.289~300 (1995)
  6. Z. Shen, "Differential Geometry of Spray and Finsler Spaces" (2001), Kluwer Academic Publishers
  7. A. Tayebi, "Some curvature properties of Cartan spaces with mth root metrics", Lith. Math. J., 54(1), pp.106~114 (2014)[DOI]
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  9. C. Yu, "On dually flat general (<TEX>${\alpha},{\beta}$<", TEX>)-metrics, 2015, pp.40, 111~122
  10. C. Yu, "On a new class of Finsler metrics", Differential Geom. Appl., 29(2), pp.244~254 (2011)[DOI]
  11. C. Yu, "Projectively flat general (<TEX>${\alpha},{\beta}$<", TEX>)-metrics with constant ag curvature, 2015, pp.429(2), 1222~1239
  12. Hongmei Zhu, "On a class of Finsler metrics with isotropic Berwald curvature", 대한수학회보, 54(2), pp.399~416 (2017), 대한수학회
  13. M. Zohrehvand, "On general <TEX>${\alpha},{\beta}$<", TEX>)-metrics of Landsberg type, 2016, pp.19(6), 1650085~

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