• Title/Summary/Keyword: (${\alpha}_1,{\alpha}_2$)-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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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 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 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 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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COMPATIBLE MAPS OF TWO TYPES AND COMMON FIXED POINT THEOREMS ON INTUITIONISTIC FUZZY METRIC SPACE

  • Park, Jong-Seo
    • Honam Mathematical Journal
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    • v.32 no.2
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    • pp.283-298
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    • 2010
  • In this paper, we introduce the concept of compatible mapping of type(${\alpha}$-1) and type(${\alpha}$-2), prove the some properties and common fixed point theorem for such maps in intuitionistic fuzzy metric space. Also, we give the example. Our research are an extension for the results of Kutukcu and Sharma[3] and Park et.al.[11].

ON CONFORMALLY FLAT POLYNOMIAL (α, β)-METRICS WITH WEAKLY ISOTROPIC SCALAR CURVATURE

  • Chen, Bin;Xia, KaiWen
    • Journal of the Korean Mathematical Society
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    • v.56 no.2
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    • pp.329-352
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    • 2019
  • In this paper, we study conformally flat (${\alpha}$, ${\beta}$)-metrics in the form $F={\alpha}(1+{\sum_{j=1}^{m}}\;a_j({\frac{\beta}{\alpha}})^j)$ with $m{\geq}2$, where ${\alpha}$ is a Riemannian metric and ${\beta}$ is a 1-form on a smooth manifold M. We prove that if such conformally flat (${\alpha}$, ${\beta}$)-metric F is of weakly isotropic scalar curvature, then it must has zero scalar curvature. Moreover, if $a_{m-1}a_m{\neq}0$, then such metric is either locally Minkowskian or Riemannian.

ON THE SECOND APPROXIMATE MATSUMOTO METRIC

  • Tayebi, Akbar;Tabatabaeifar, Tayebeh;Peyghan, Esmaeil
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.1
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    • pp.115-128
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    • 2014
  • In this paper, we study the second approximate Matsumoto metric F = ${\alpha}+{\beta}+{\beta}^2/{\alpha}+{\beta}^3/{\alpha}^2$ on a manifold M. We prove that F is of scalar flag curvature and isotropic S-curvature if and only if it is isotropic Berwald metric with almost isotropic flag curvature.

WEAKLY BERWALD SPACE WITH A SPECIAL (α, β)-METRIC

  • PRADEEP KUMAR;AJAYKUMAR AR
    • Honam Mathematical Journal
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    • v.45 no.3
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    • pp.491-502
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    • 2023
  • As a generalization of Berwald spaces, we have the ideas of Douglas spaces and Landsberg spaces. S. Bacso defined a weakly-Berwald space as another generalization of Berwald spaces. In 1972, Matsumoto proposed the (α, β) metric, which is a Finsler metric derived from a Riemannian metric α and a differential 1-form β. In this paper, we investigated an important class of (α, β)-metrics of the form $F={\mu}_1\alpha+{\mu}_2\beta+{\mu}_3\frac{\beta^2}{\alpha}$, which is recognized as a special form of the first approximate Matsumoto metric on an n-dimensional manifold, and we obtain the criteria for such metrics to be weakly-Berwald metrics. A Finsler space with a special (α, β)-metric is a weakly Berwald space if and only if Bmm is a 1-form. We have shown that under certain geometric and algebraic circumstances, it transforms into a weakly Berwald space.