• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.567-589
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• 2004

In the present paper, we treat an infinite series ($\alpha$, $\beta$)-metric L =$\beta$$^2$/($\beta$-$\alpha$). First, we find the conditions that a Finsler metric F$^{n}$ with the metric above be a Berwald space, a Douglas space, and a projectively flat Finsler space, respectively. Next, we investigate the condition that a two-dimensional Finsler space with the metric above be a Landsbeg space. Then the differential equations of the geodesics are also discussed.

• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.373-383
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• 1999

The ($\alpha$,$\beta$)-metric is a Finsler metric which is constructed from a Riemannian metric $\alpha$ and a differential 1-from $\beta$;it has been sometimes treated in theoretical physics. The condition for a Finsler space with an ($\alpha$,$\beta$)-metric L($\alpha$,$\beta$) to be projectively flat was given by Matsumoto [11]. The present paper is devoted to studying the condition for a Finsler space with L=$\alpha$\ulcorner$\beta$\ulcorner or L=$\alpha$+$\beta$\ulcorner/$\alpha$ to be projectively flat on the basis of Matsumoto`s results.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.501-513
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• 2003

The Matsumoto metric is an ($\alpha,\;\bata$)-metric which is an exact formulation of the model of Finsler space. Lately, this metric was expressed as an infinite series form for $$\mid$\beat$\mid$\;<\;$\mid$\alpha$\mid$$ by the first author. He introduced an approximate Matsumoto metric as the ($\alpha,\;\bata$)-metric of finite series form and investigated it in [11]. The purpose of the present paper is devoted to finding the condition for a Finsler space with an approximate Matsumoto metric to be projectively flat.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.355-364
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• 1997

In a Finsler space, we introduce a special $(\alpha,\beta)$-metric L satisfying $L^2(\alpha,\beta) = c_1\alpha^2 + 2c_2\alpha\beta + c_3\beta^2$, which $c_i$ are constants. We investigate the Berwald connection in a Finsler space with this special $\alpha,\beta)$-metric.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.399-416
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• 2017

In this paper, we study a class of Finsler metrics called general (${\alpha},{\beta}$)-metrics, which are defined by a Riemannian metric ${\alpha}$ and a 1-form ${\beta}$. We show that every general (${\alpha},{\beta}$)-metric with isotropic Berwald curvature is either a Berwald metric or a Randers metric. Moreover, a lot of new isotropic Berwald general (${\alpha},{\beta}$)-metrics are constructed explicitly.

• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.201-210
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• 1999

We introduce the notion of the Finsler metrics compatible with f(5,1)-structure and investigate the properties of Finsler space with such metrics.

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.23-31
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• 1999

The purpose of the present paper is devoted to a study of some properties on spaces with a quartic metric from the standpoint of Finsler geometry.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.183-200
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• 2012

In the present paper, we consider the condition that is a geodesic equation on a Finsler space with an (${\alpha},\;{\beta}$)-metric. Next we find the conditions that are equations of geodesic on the Finsler space with an approximate infinite series (${\alpha},\;{\beta}$)-metric.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.975-984
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• 1997

In the Finsler space with an $(\alpha, \beta)$-metric, we can consider the difference tensors of the Finsler connection. The properties of the conformal transformation of these difference tensors are investigated in the present paper. Some conformal invariant tensors are formed in the Finsler space with an $(\alpha, \beta)$-metric related with the difference tensors.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.699-716
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• 2009

We deal with a Finsler space $F^n$ with an approximate infinite series $({\alpha},\;{\beta})$-metric $L({\alpha},\;{\beta})$ = ${\beta}{\sum}_{k=0}^{r}(\frac{\alpha}{\beta})^k$ where ${\alpha}<{\beta}$. We introduced a Finsler space $F^n$ with an infinite series $({\alpha},{\beta})$-metric $L({\alpha},\;{\beta})=\frac{\beta^2}{\beta-\alpha}$ and investigated various geometrical properties at [6]. The purpose of the present paper is devoted to finding the condition for a Finsler space $F^n$ with an approximate infinite series $({\alpha},\;{\beta})$-metric above to be a Douglas space.