• Title/Summary/Keyword: Berwald metric

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TWO CLASSES OF THE GENERALIZED RANDERS METRIC

  • Choi, Eun-Seo;Kim, Byung-Doo
    • 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.

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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 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.

THE m-TH ROOT FINSLER METRICS ADMITTING (α, β)-TYPES

  • Kim, Byung-Doo;Park, Ha-Yong
    • Bulletin of the Korean Mathematical Society
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    • v.41 no.1
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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.

Conformal transformations of difference tensors of Finsler space with an $(alpha,beta)$-metric

  • Lee, Yong-Duk
    • 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.

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ON THE LANDSBERG SPACES OF DIMENSION TWO WITH A SPECIAL ($\alpha$, $\beta$)-METRIC

  • Park, Hong-Suh;Lee, Il-Yong
    • Journal of the Korean Mathematical Society
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    • v.37 no.1
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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.

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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 PROJECTIVELY FLAT FINSLER SPACES WITH $({\alpha},{\beta})$-METRIC

  • Park, Hong-Suh;Lee, Il-Yong
    • Communications of the Korean Mathematical Society
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    • v.14 no.2
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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.

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