• 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.

• 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.

• 대한수학회지
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• 제37권1호
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• pp.73-84
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• 2000

The present paper is devoted to studying the condition that a two-dimensional Finsler space with a special (${\alpha}$, ${\beta}$)-metric be a Landsberg space. It is proved that if a Finsler space with a special (${\alpha}$, ${\beta}$)-metric is a Landsberg space, then it is a Berwald space.

• East Asian mathematical journal
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• 제15권1호
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• pp.81-90
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• 1999

• 한국전산응용수학회:학술대회논문집
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• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
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• pp.5.2-5
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• 2003

In this paper, we are to find the condition that a two-dimensional Finsler space with Matsumoto metric satisfying L(${\alpha}$,${\beta}$)=${\alpha}$$^2$/(${\alpha}$-${\beta}$) be a Landsberg space and the differential equations of geodesics.

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

• 호남수학학술지
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• 제45권3호
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• pp.491-502
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• 2023

As a generalization of Berwald spaces, we have the ideas of Douglas spaces and Landsberg spaces. S. Bacso defined a weakly-Berwald space as another generalization of Berwald spaces. In 1972, Matsumoto proposed the (α, β) metric, which is a Finsler metric derived from a Riemannian metric α and a differential 1-form β. In this paper, we investigated an important class of (α, β)-metrics of the form $F={\mu}_1\alpha+{\mu}_2\beta+{\mu}_3\frac{\beta^2}{\alpha}$, which is recognized as a special form of the first approximate Matsumoto metric on an n-dimensional manifold, and we obtain the criteria for such metrics to be weakly-Berwald metrics. A Finsler space with a special (α, β)-metric is a weakly Berwald space if and only if B^m_m is a 1-form. We have shown that under certain geometric and algebraic circumstances, it transforms into a weakly 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.

• 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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• 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.