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http://dx.doi.org/10.4134/BKMS.b170710

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.55, no.4, 2018 , pp. 1231-1240 More about this Journal
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.
Keywords
Finsler metric; (${\alpha},{\beta}$)-metric; conformal transformation; the mean Landsberg curvature;
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