• Title, Summary, Keyword: the second approximate Matsumoto metric

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ON A HYPERSURFACE OF THE FIRST APPROXIMATE MATSUMOTO SPACE

  • Lee, Il-Yong;Jun, Dong-Gum
    • East Asian mathematical journal
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    • v.17 no.2
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    • pp.325-337
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    • 2001
  • We consider the special hypersurface of the first approximate Matsumoto metric with $b_i(x)={\partial}_ib$ being the gradient of a scalar function b(x). In this paper, we consider the hypersurface of the first approximate Matsumoto space with the same equation b(x)=constant. We are devoted to finding the condition for this hypersurface to be a hyperplane of the first or second kind. We show that this hypersurface is not a hyper-plane of third kind.

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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.