Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON CONFORMAL TRANSFORMATIONS BETWEEN TWO ALMOST REGULAR (α, β)-METRICS

  • Chen, Guangzu (School of Science East China JiaoTong University) ;
  • Liu, Lihong (School of Science East China JiaoTong University)
  • Received : 2017.08.11
  • Accepted : 2018.03.13
  • Published : 2018.07.31
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Abstract

In this paper, we characterize the conformal transformations between two almost regular (${\alpha},{\beta}$)-metrics. Suppose that F is a non-Riemannian (${\alpha},{\beta}$)-metric and is conformally related to ${\widetilde{F}}$, that is, ${\widetilde{F}}=e^{{\kappa}(x)}F$, where ${\kappa}:={\kappa}(x)$ is a scalar function on the manifold. We obtain the necessary and sufficient conditions of the conformal transformation between F and ${\widetilde{F}}$ preserving the mean Landsberg curvature. Further, when both F and ${\widetilde{F}}$ are regular, the conformal transformation between F and ${\widetilde{F}}$ preserving the mean Landsberg curvature must be a homothety.

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