• Title/Summary/Keyword: infinite series (${\alpha},{\beta}$)-metric 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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EQUATIONS OF GEODESIC WITH AN APPROXIMATE INFINITE SERIES (${\alpha},{\beta}$)-METRIC

  • Lee, Il-Yong
    • Journal of the Chungcheong Mathematical Society
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    • v.25 no.2
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    • pp.183-200
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    • 2012
  • In the present paper, we consider the condition that is a geodesic equation on a Finsler space with an (${\alpha},\;{\beta}$)-metric. Next we find the conditions that are equations of geodesic on the Finsler space with an approximate infinite series (${\alpha},\;{\beta}$)-metric.

ON PROJECTIVELY FLAT FINSLER SPACE WITH AN APPROXIMATE INFINITE SERIES (α,β)-METRIC

  • Lee, Il-Yong
    • East Asian mathematical journal
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    • v.28 no.1
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    • pp.25-36
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    • 2012
  • We introduced a Finsler space $F^n$ with an approximate infinite series (${\alpha},{\beta}$-metric $L({\alpha},{\beta})={\beta}\sum\limits_{k=0}^r\(\frac{\alpha}{\beta}\)^k$, where ${\alpha}<{\beta}$ and investigated it with respect to Berwald space ([12]) and Douglas space ([13]). The present paper is devoted to finding the condition that is projectively at on a Finsler space $F^n$ with an approximate infinite series (${\alpha},{\beta}$)-metric above.

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 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.