• Title, Summary, Keyword: Douglas 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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ON THE CLASS OF COMPLEX DOUGLAS-KROPINA SPACES

  • Aldea, Nicoleta;Munteanu, Gheorghe
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.1
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    • pp.251-266
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    • 2018
  • In this paper, considering the class of complex Kropina metrics we obtain the necessary and sufficient conditions that these are generalized Berwald and complex Douglas metrics, respectively. Special attention is devoted to a class of complex Douglas-Kropina spaces, in complex dimension 2. Also, some examples of complex Douglas-Kropina metrics are pointed out. Finally, the complex Douglas-Kropina metrics are characterized through the theory of projectively related complex Finsler metrics.

FINSLER SPACES WITH CERTAIN ($\alpha$,$\beta$)-METRIC OF DOUGLAS TYPE

  • Park, Hong-Suh;Lee, Yong-Duk
    • Communications of the Korean Mathematical Society
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    • v.16 no.4
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    • pp.649-658
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    • 2001
  • We shall find the condition for a Finsler space with a special ($\alpha$.$\beta$)-metric L($\alpha$.$\beta$) satisfying L$^2$ =2$\alpha$$\beta$ to be a Douglas space. The special Randers change of the above Finsler metric by $\beta$ is also studied.

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ON DOUGLAS SPACE WITH AN APPROXIMATE INFINITE SERIES (α,β)-METRIC

  • Lee, Il-Yong
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.4
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    • pp.699-716
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    • 2009
  • We deal with a Finsler space $F^n$ with an approximate infinite series $({\alpha},\;{\beta})$-metric $L({\alpha},\;{\beta})$ = ${\beta}{\sum}_{k=0}^{r}(\frac{\alpha}{\beta})^k$ where ${\alpha}<{\beta}$. We introduced a Finsler space $F^n$ with an infinite series $({\alpha},{\beta})$-metric $L({\alpha},\;{\beta})=\frac{\beta^2}{\beta-\alpha}$ and investigated various geometrical properties at [6]. The purpose of the present paper is devoted to finding the condition for a Finsler space $F^n$ with an approximate infinite series $({\alpha},\;{\beta})$-metric above to be a Douglas space.

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ON WEAKLY-BERWALD SPACES OF SPECIAL (α, β)-METRICS

  • Lee, Il-Yong;Lee, Myung-Han
    • Bulletin of the Korean Mathematical Society
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    • v.43 no.2
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    • pp.425-441
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    • 2006
  • We have two concepts of Douglas spaces and Lands-berg spaces as generalizations of Berwald spaces. S. Bacso gave the definition of a weakly-Berwald space [2] as another generalization of Berwald spaces. In the present paper, we find the conditions that the Finsler space with an (${\alpha},{\beta}$)-metric be a weakly-Berwald space and the Finsler spaces with some special (${\alpha},{\beta}$)-metrics be weakly-Berwald spaces, respectively.

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.

THE RANDER CHANGES OF FINSLER SPACES WITH ($\alpha,\beta$)-METRICS OF DOUGLAS TYPE

  • Park, Hong-Suh;Lee, Il-Yong
    • Journal of the Korean Mathematical Society
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    • v.38 no.3
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    • pp.503-521
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    • 2001
  • A change of Finsler metric L(x,y)longrightarrowL(x,y) is called a Randers change of L, if L(x,y) = L(x,y) +$\rho$(x,y), where $\rho$(x,y) = $\rho$(sub)i(x)y(sup)i is a 1-form on a smooth manifold M(sup)n. Let us consider the special Randers change of Finsler metric LlongrightarrowL = L + $\beta$ by $\beta$. On the basis of this special Randers change, the purpose of the present paper is devoted to studying the conditions for Finsler space F(sup)n which are transformed by a special Randers change of Finsler spaces F(sup)n with ($\alpha$,$\beta$)-metrics of Douglas type to be also of Douglas type, and vice versa.

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On Special finsler Spaces With Common Geodesics

  • Kim, Byung-Doo;Park, Ha-Yong
    • Communications of the Korean Mathematical Society
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    • v.15 no.2
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    • pp.331-338
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    • 2000
  • In the present paper, we investigate a problem in a sym-metric Finsler space, which is a special space. First we prove that if a symmetric space remains to be a symmetric one under the Z-projective change, then the space is of zero curvature. Further we will study W-recurrent space and D-recurrent space under the pro-jective change.

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