• 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.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.457-464
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• 2003

Given a Riemannian manifold (M, $\alpha$) with an almost Hermitian structure f and a non-vanishing covariant vector field b, consider the generalized Randers metric $L\;=\;{\alpha}+{\beta}$, where $\beta$ is a special singular Riemannian metric defined by b and f. This metric L is called an (a, b, f)-metric. We compute the inverse and the determinant of the fundamental tensor ($g_{ij}$) of an (a, b, f)-metric. Then we determine the maximal domain D of $TM{\backslash}O$ for an (a, b, f)-manifold where a y-local Finsler structure L is defined. And then we show that any (a, b, f)-manifold is quasi-C-reducible and find a condition under which an (a, b, f)-manifold is C-reducible.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.975-984
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• 1997

In the Finsler space with an $(\alpha, \beta)$-metric, we can consider the difference tensors of the Finsler connection. The properties of the conformal transformation of these difference tensors are investigated in the present paper. Some conformal invariant tensors are formed in the Finsler space with an $(\alpha, \beta)$-metric related with the difference tensors.

• Journal of the Korean Mathematical Society
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• v.37 no.1
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• pp.73-84
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• 2000

The present paper is devoted to studying the condition that a two-dimensional Finsler space with a special (${\alpha}$, ${\beta}$)-metric be a Landsberg space. It is proved that if a Finsler space with a special (${\alpha}$, ${\beta}$)-metric is a Landsberg space, then it is a Berwald space.

• 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.

• Journal of the Korean Mathematical Society
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• v.55 no.2
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• pp.415-424
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• 2018

General (${\alpha},\;{\beta}$)-metrics form a rich and important class of Finsler metrics. In this paper, we obtain a differential equation which characterizes a general (${\alpha},\;{\beta}$)-metric with isotropic E-curvature, under a certain condition. We also solve the equation in a particular case.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.407-418
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• 2019

In this paper, we study conformal transformations between special class of Finsler metrics named C-reducible metrics. This class includes Randers metrics in the form $F={\alpha}+{\beta}$ and Kropina metric in the form $F={\frac{{\alpha}^2}{\beta}}$. We prove that every conformal transformation between locally dually flat Randers metrics must be homothetic and also every conformal transformation between locally dually flat Kropina metrics must be homothetic.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.781-788
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• 2018

In the present paper, we have studied the Finslerian hypersurfaces and generalized ${\beta}$-conformal change of Finsler metric. The relations between the Finslerian hypersurface and the other which is Finslerian hypersurface given by generalized ${\beta}$-conformal change have been obtained. We have also proved that generalized ${\beta}$-conformal change makes three types of hypersurfaces invariant under certain conditions.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.14 no.1
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• pp.66-72
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• 2014

In this paper, we establish common fixed point theorem for type(${\beta}$) compatible four mappings with implicit relations defined on an intuitionistic fuzzy metric space. Also, we present the example of common fixed point satisfying the conditions of main theorem in an intuitionistic fuzzy metric space.

• Kyungpook Mathematical Journal
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• v.63 no.4
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• pp.611-622
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• 2023

In this paper, we prove that every weakly Einstein slope metric, which is conformally flat on a manifold M of dimension n ≥ 3, is either a locally Minkowski metric or a Riemannian metric. We also prove the same result for conformally flat weakly Einstein Kropina metrics.