• Korean Journal of Mathematics
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• v.18 no.4
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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.

• East Asian mathematical journal
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• v.17 no.2
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• pp.325-337
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• 2001

We consider the special hypersurface of the first approximate Matsumoto metric with $b_i(x)={\partial}_ib$ being the gradient of a scalar function b(x). In this paper, we consider the hypersurface of the first approximate Matsumoto space with the same equation b(x)=constant. We are devoted to finding the condition for this hypersurface to be a hyperplane of the first or second kind. We show that this hypersurface is not a hyper-plane of third kind.

• Honam Mathematical Journal
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• v.29 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.251-266
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• 2018

In this paper, considering the class of complex Kropina metrics we obtain the necessary and sufficient conditions that these are generalized Berwald and complex Douglas metrics, respectively. Special attention is devoted to a class of complex Douglas-Kropina spaces, in complex dimension 2. Also, some examples of complex Douglas-Kropina metrics are pointed out. Finally, the complex Douglas-Kropina metrics are characterized through the theory of projectively related complex Finsler metrics.