• Title, Summary, Keyword: ($\alpha, \beta$)-metric

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ON THE BERWALD CONNECTION OF A FINSLER SPACE WITH A SPECIAL $({\alpha},{\beta})$-METRIC

  • Park, Hong-Suh;Park, Ha-Yong;Kim, Byung-Doo
    • 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.

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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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Projective Change between Two Finsler Spaces with (α, β)- metric

  • Kampalappa, Narasimhamurthy Senajji;Mylarappa, Vasantha Dogehalli
    • Kyungpook Mathematical Journal
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    • v.52 no.1
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    • pp.81-89
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    • 2012
  • In the present paper, we nd the conditions to characterize projective change between two (${\alpha}$, ${\beta}$)-metrics, such as Matsumoto metric $L=\frac{{\alpha}^2}{{\alpha}-{\beta}}$ and Randers metric $\bar{L}=\bar{\alpha}+\bar{\beta}$ on a manifold with dim $n$ > 2, where ${\alpha}$ and $\bar{\alpha}$ are two Riemannian metrics, ${\beta}$ and $\bar{\beta}$ are two non-zero 1-formas.

On the projectively flat finsler space with a special $(alpha,beta)$-metric

  • Kim, Byung-Doo
    • Communications of the Korean Mathematical Society
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    • v.11 no.2
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    • pp.407-413
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    • 1996
  • The $(\alpha, \beta)$-metric is a Finsler metric which is constructed from a Riemannian metric $\alpha$ and a differential 1-form $\Beta$; it has been sometimes treat in theoretical physics. In particular, the projective flatness of Finsler space with a metric $L^2 = 2\alpha\beta$ is considered in detail.

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ON A CLASS OF FINSLER METRICS WITH ISOTROPIC BERWALD CURVATURE

  • Zhu, Hongmei
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.2
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    • pp.399-416
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    • 2017
  • In this paper, we study a class of Finsler metrics called general (${\alpha},{\beta}$)-metrics, which are defined by a Riemannian metric ${\alpha}$ and a 1-form ${\beta}$. We show that every general (${\alpha},{\beta}$)-metric with isotropic Berwald curvature is either a Berwald metric or a Randers metric. Moreover, a lot of new isotropic Berwald general (${\alpha},{\beta}$)-metrics are constructed explicitly.

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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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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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 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.

PROJECTIVELY FLAT FINSLER SPACES WITH CERTAIN (α, β)-METRICS

  • Park, Hong-Suh;Park, Ha-Yong;Kim, Byung-Doo;Choi, Eun-Seo
    • Bulletin of the Korean Mathematical Society
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    • v.40 no.4
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    • pp.649-661
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    • 2003
  • The ($\alpha,\;\beta$)-metric is a Finsler metric which is constructed from a Riemannian metric $\alpha$ and a differential 1-form $\beta$. In this paper, we discuss the projective flatness of Finsler spaces with certain ($\alpha,\;\beta$)-metrics ([5]) in a locally Minkowski space.