• Title, Summary, Keyword: locally Minkowski space

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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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HOMOGENEOUS FUNCTION AND ITS APPLICATION IN A FINSLER SPACE

  • Kim, Byung-Doo;Choi, Eun-Seo
    • Communications of the Korean Mathematical Society
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    • v.14 no.2
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    • pp.385-392
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    • 1999
  • We deal with a differential equation which is constructed from homogeneous function, and its geometrical meaning in a Finsler space. Moreover, were prove that a locally Minkowski space satisfying a differential equation F\ulcorner=0 is flat-parallel.

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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.

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.

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.

REEB FLOW SYMMETRY ON ALMOST COSYMPLECTIC THREE-MANIFOLDS

  • Cho, Jong Taek
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.4
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    • pp.1249-1257
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    • 2016
  • We prove that the Ricci operator S of an almost cosymplectic three-manifold M is invariant along the Reeb flow, that is, M satisfies ${\pounds}_{\xi}S=0$ if and only if M is either cosymplectic or locally isometric to the group E(1, 1) of rigid motions of Minkowski 2-space with a left invariant almost cosymplectic structure.