• Kyungpook Mathematical Journal
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• 제63권4호
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• pp.611-622
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• 2023

In this paper, we prove that every weakly Einstein slope metric, which is conformally flat on a manifold M of dimension n ≥ 3, is either a locally Minkowski metric or a Riemannian metric. We also prove the same result for conformally flat weakly Einstein Kropina metrics.

• 호남수학학술지
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• 제29권4호
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• pp.617-630
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• 2007

In this paper, we'll introduce infinitesimal Finsler metrics induced by the higher order Kobayashi pseudometric and then prove some properties related to these as compared with the usual Kobayashi metric.

• 대한수학회보
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• 제54권3호
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• pp.967-973
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• 2017

We prove that a homogeneous square Einstein Finsler metric is either Riemannian or flat.

• East Asian mathematical journal
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• 제19권2호
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• pp.261-271
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• 2003

We deal with two metrics of Randers type, which are characterized by the solution of certain differential equations respectively. Furthermore, we will give the condition for a Finsler space with such a metric to be a locally Minkowski space or a conformally flat space, respectively.

• Korean Journal of Mathematics
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• 제18권4호
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• pp.387-394
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• 2010

In this paper, we study the generalized Randers change $^*L(x,y)=L(x,y)+b_i(x,y)y^i$ from the Brewald metric L and the h-vector $b_i$. And in search for a non-Berwald Landsberg metric, we obtain the conditions on $b_i(x,y)$ under which $^*L$ is a Landsberg metric.

• 대한수학회보
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• 제55권4호
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• pp.1231-1240
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• 2018

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.