• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1293-1307
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• 2017

General (${\alpha},{\beta}$)-metrics form a rich class of Finsler metrics. They include many important Finsler metrics, such as Randers metrics, square metrics and spherically symmetric metrics. In this paper, we find equations which are necessary and sufficient conditions for such Finsler metric to be locally projectively flat. By solving these equations, we obtain all of locally projectively flat general (${\alpha},{\beta}$)-metrics under certain condition. Finally, we manufacture explicitly new locally projectively flat Finsler metrics.

• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.201-210
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• 1999

We introduce the notion of the Finsler metrics compatible with f(5,1)-structure and investigate the properties of Finsler space with such metrics.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.1-7
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• 2020

In this paper, it is shown that the reversible harmonic Finsler metrics on spheres must be Riemannian.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1641-1650
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• 2023

It is our goal in this study to present the structure of isotropic mean Berwald Finsler warped product metrics. We bring out the rich class of warped product Finsler metrics behaviour under this condition. We show that every Finsler warped product metric of dimension n ≥ 2 is of isotropic mean Berwald curvature if and only if it is a weakly Berwald metric. Also, we prove that every locally dually flat Finsler warped product metric is weakly Berwaldian. Finally, we prove that every Finsler warped product metric is of isotropic Berwald curvature if and only if it is a Berwald metric.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.639-648
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• 2013

In this paper, we study Finsler metrics of constant S-curvature. First we produce infinitely many Randers metrics with non-zero (constant) S-curvature which have vanishing H-curvature. They are counterexamples to Theorem 1.2 in [20]. Then we show that the existence of (${\alpha}$, ${\beta}$)-metrics with arbitrary constant S-curvature in each dimension which is not Randers type by extending Li-Shen' construction.

• 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.

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.339-348
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• 2000

We introduce the notion of the Finsler metrics compat-ible with a special Riemannian structure f of type (1,1) satisfying f6+f2=0 and investigate the properties of Finsler space with them.

• 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.

• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.353-362
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• 2019

In this paper, we study general (${\alpha}$, ${\beta}$) Finsler metrics and prove that every general (${\alpha}$, ${\beta}$)-metric is semi C-reducible but not C2-like. As a consequence of this result we prove that every general (${\alpha}$, ${\beta}$)-metric satisfying the Ricci flow equation is Einstein.

• 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.