• 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.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.383-391
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• 1997

The main purpose of the present paper is to derive the induced (Finsler) connections on the hypersurface from the Finsler connections of Berwald type (a Berwald h-recurrent connection and a $F\Gamma$' 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 quantities and relations with respect to the respective induced connections. Finally we show some examples.

• The Pure and Applied Mathematics
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• v.10 no.4
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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.

• East Asian mathematical journal
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• v.19 no.2
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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.

• Journal for History of Mathematics
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• v.31 no.1
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• pp.37-51
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• 2018

In this paper, our main concern is the historical development of the Finsler geometry in Debrecen, Hungary initiated by L. Berwald. First we look into the research trend in Berwald's days affected by the $G{\ddot{o}}ttingen$ mathematicians from C. Gauss and downward. Then we study how he was motivated to concentrate on the then completely new research area, Finsler geometry. Finally we examine the course of establishing Hungarian Debrecen school of Finsler geometry via the scholars including O. Varga, A. $Rapcs{\acute{a}}k$, L. $Tam{\acute{a}}ssy$ all deeply affected by Berwald after his settlement in Debrecen, Hungary.

• East Asian mathematical journal
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• v.15 no.1
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• pp.81-90
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• 1999

• 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.

• 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.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.593-607
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• 2021

The aim of the present paper is to establish an intrinsic generalization of Cartan connection in Finsler geometry. This connection is called the vertical recurrent Finsler connection. An intrinsic proof of the existence and uniqueness theorem for such connection is investigated. Moreover, it is shown that for such connection, the associated semi-spray coincides with the canonical spray and the associated nonlinear connection coincides with the Barthel connection. Explicit intrinsic expression relating this connection and Cartan connection is deduced. We also investigate some applications concerning the fundamental geometric objects associated with this connection. Finally, three important results concerning the curvature tensors associated to a special vertical recurrent Finsler connection are studied.

• East Asian mathematical journal
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• v.19 no.2
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• pp.261-271
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• 2003

We deal with two metrics of Randers type, which are characterized by the solution of certain differential equations respectively. Furthermore, we will give the condition for a Finsler space with such a metric to be a locally Minkowski space or a conformally flat space, respectively.