• 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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• 제14권2호
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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.

• 한국수학사학회지
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• 제34권2호
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• pp.55-74
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• 2021

Matsumoto Makoto is regarded as founding father of the Japanese school of Finsler geometry because he established the Japanese Society of Finsler Geometry in 1968 and organized the Symposium every year since then. In this paper, we investigate how Matsumoto initiated the study of this topic leaping over geographical limit and how Yano Kentaro and Kawaguchi Akitsugu had affected Matsumoto in the formation of the Japanese school of Finsler geometry. We also take a view of the role of É. Cartan who invented the concept of the connection in early 20th century in this regard.

• 대한수학회보
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• 제39권1호
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• pp.153-163
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• 2002

The present paper is devoted to studying the condition for a Finsler space with the second approximate Matsumoto metric to be a Berwald space and to be a Douglas space.

• 대한수학회보
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• 제41권1호
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• pp.45-52
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• 2004

The theory of m-th root metric has been developed by H. Shimada [8], and applied to the biology [1] as an ecological metric. The purpose of this paper is to introduce the m-th root Finsler metrics which admit ($\alpha,\;\beta$)-types. Especially in cases of m = 3, 4, we give the condition for Finsler spaces with such metrics to be locally Minkowski spaces.

• 대한수학회보
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• 제50권2호
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• pp.639-648
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• 2013

In this paper, we study Finsler metrics of constant S-curvature. First we produce infinitely many Randers metrics with non-zero (constant) S-curvature which have vanishing H-curvature. They are counterexamples to Theorem 1.2 in [20]. Then we show that the existence of (${\alpha}$, ${\beta}$)-metrics with arbitrary constant S-curvature in each dimension which is not Randers type by extending Li-Shen' construction.

• 대한수학회논문집
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• 제12권2호
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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.

• 대한수학회논문집
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• 제11권2호
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• pp.423-443
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• 1996

The main purposer of the present paper is to derive the induced (Finsler) connections on the hypersurface from the Finsler connections of Cartan type (a Wagner, Miron, Cartan C- and Cartan Y- connection) of a Finsler space and to seek the necessary and sufficient conditions that the induced connections coincide with the intrinsic connections. And we show the differences of quantities with respect to the respective a connections and an induced Cartan connection. Finally we show some examples.

• 대한수학회보
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• 제54권2호
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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.

• Journal of applied mathematics & informatics
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• 제5권3호
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• pp.839-848
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• 1998

We can obtain the concise description of two dimensional Finsler space from the viewpoint of their geodesic curves. In this paper we obtain the geodesic equations in a two-dimensional Finsler space with some special (${\alpha},\;{\beta}$)-metrics by using the Weierstrass form. We shall be referred to an isothermal coodinate system and an orthonormal one with respect to an associated Riemannian space.