• Title, Summary, Keyword: Finsler space

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ON TWO-DIMENSIONAL LANDSBERG SPACE OF A CUBIC FINSLER SPACE

  • Lee, Il-Yong;Jun, Dong-Gum
    • 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.

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DOUGLAS SPACES OF THE SECOND KIND OF FINSLER SPACE WITH A MATSUMOTO METRIC

  • Lee, Il-Yong
    • Journal of the Chungcheong Mathematical Society
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    • v.21 no.2
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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.

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FINSLER SPACES WITH INFINITE SERIES (α, β)-METRIC

  • Lee, Il-Yong;Park, Hong-Suh
    • 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.

ON SOME CLASSES OF ℝ-COMPLEX HERMITIAN FINSLER SPACES

  • Aldea, Nicoleta;Campean, Gabriela
    • Journal of the Korean Mathematical Society
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    • v.52 no.3
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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.

ON A FINSLER SPACE WITH (α, β)-METRIC AND CERTAIN METRICAL NON-LINEAR CONNECTION

  • PARK HONG-SUH;PARK HA-YONG;KIM BYUNG-DOO
    • Communications of the Korean Mathematical Society
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    • v.21 no.1
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    • pp.177-183
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    • 2006
  • The purpose of this paper is to introduce an L-metrical non-linear connection $N_j^{*i}$ and investigate a conformal change in the Finsler space with $({\alpha},\;{\beta})-metric$. The (v)h-torsion and (v)hvtorsion in the Finsler space with L-metrical connection $F{\Gamma}^*$ are obtained. The conformal invariant connection and conformal invariant curvature are found in the above Finsler space.

ON TWO-DIMENSIONAL LANDSBERG SPACE WITH A SPECIAL (${\alpha},\;{\beta}$)-METRIC

  • Lee, Il-Yong
    • 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.

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SOME PROPERTIES ON FINSLER SPACES WITH A QUARTIC METRIC

  • Lee, Il-Yong;Jun, Dong-Gum
    • 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.

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A Finsler space with a special metric function

  • Park, Hong-Suh;Lee, Il-Young
    • Communications of the Korean Mathematical Society
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    • v.11 no.2
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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.

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