• East Asian mathematical journal
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• 제19권2호
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• pp.305-316
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• 2003

In the present paper, we are to find the conditions that a cubic Finsler space is a Berwald space and a two-dimensional cubic Finsler space is a Landsberg space. It is shown that if a two-dimensional cubic Finsler space is a Landsberg space, then it is a Berwald space.

• 충청수학회지
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• 제21권2호
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• pp.209-221
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• 2008

In the present paper, first we define a Douglas space of the second kind of a Finsler space with an (${\alpha},{\beta}$)-metric. Next we find the conditions that the Finsler space with an (${\alpha},{\beta}$)-metric be a Douglas space of the second kind and the Finsler space with a Matsumoto metric be a Douglas space of the second kind.

• 대한수학회지
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• 제52권3호
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• pp.587-601
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• 2015

In this paper, we investigate the $\mathbb{R}$-complex Hermitian Finsler spaces, emphasizing the differences that separate them from the complex Finsler spaces. The tools used in this study are the Chern-Finsler and Berwald connections. By means of these connections, some classes of the $\mathbb{R}$-complex Hermitian Finsler spaces are defined, (e.g. weakly K$\ddot{a}$hler, K$\ddot{a}$hler, strongly K$\ddot{a}$hler). Here the notions of K$\ddot{a}$hler and strongly K$\ddot{a}$hler do not coincide, unlike the complex Finsler case. Also, some kinds of Berwald notions for such spaces are introduced. A special approach is devoted to obtain the equivalence conditions for an $\mathbb{R}$-complex Hermitian Finsler space to become a weakly Berwald or Berwald. Finally, we obtain the conditions under which an $\mathbb{R}$-complex Hermitian Finsler space with Randers metric is Berwald. We get some clear examples which illustrate the interest for this work.

• East Asian mathematical journal
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• 제16권2호
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• pp.339-354
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• 2000

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제10권4호
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• pp.279-288
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• 2003

In the present paper, we treat a Finsler space with a special (${\alpha},\;{\beta}$)-metric $L({\alpha},\;{\beta})\;\;C_1{\alpha}＋C_2{\beta}+{\alpha}^2/{\beta}$ satisfying some conditions. We find a condition that a Finsler space with a special (${\alpha},\;{\beta}$)-metric be a Berwald space. Then it is shown that if a two-dimensional Finsler space with a special (${\alpha},\;{\beta}$)-metric is a Landsberg space, then it is a Berwald space.

• 충청수학회지
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• 제12권1호
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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.

• 대한수학회지
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• 제41권3호
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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.

• 대한수학회논문집
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• 제11권2호
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• pp.415-421
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• 1996

In this paper, we shall find the conditions that the Finsler space with a special $(\alpha,\beta)$-metric be a Riemannian space and a Berwald space.

• 대한수학회논문집
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• 제12권4호
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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.

• 대한수학회보
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• 제40권4호
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• pp.649-661
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• 2003

The ($\alpha,\;\beta$)-metric is a Finsler metric which is constructed from a Riemannian metric $\alpha$ and a differential 1-form $\beta$. In this paper, we discuss the projective flatness of Finsler spaces with certain ($\alpha,\;\beta$)-metrics ([5]) in a locally Minkowski space.