• 대한수학회보
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• 제50권2호
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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.

• Journal of applied mathematics & informatics
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• 제41권3호
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• pp.603-613
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• 2023

In this paper, the concept of geodesic centered tractography is explored for diffusion tensor imaging (DTI). In DTI, where geodesics has been tracked and the inverse of the fourth-order diffusion tensor is inured to determine the diversity. Specifically, we investigated geodesic tractography technique for High Angular Resolution Diffusion Imaging (HARDI). Riemannian geometry can be extended to a direction-dependent metric using Finsler geometry. Euler Lagrange geodesic calculations have been derived by Finsler geometry, which is expressed as HARDI in sixth order tensor.

• 대한수학회보
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• 제57권6호
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• pp.1335-1349
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• 2020

In this paper, we give an equivalent characterization for general (α, β)-metrics with reversible geodesics when the dimension of the manifold is greater than 2.

• 대한수학회지
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• 제44권1호
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• pp.237-247
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• 2007

In this paper, we establish a necessary condition in terms of curvature for the Kobayashi hyperbolicity of a class of almost complex Finsler manifolds. For an almost complex Finsler manifold with the condition (R), so-called Rizza manifold, we show that there exists a unique connection compatible with the metric and the almost complex structure which has the horizontal torsion in a special form. With this connection, we define a holomorphic sectional curvature. Then we show that this holomorphic sectional curvature of an almost complex submanifold is not greater than that of the ambient manifold. This fact, in turn, implies that a Rizza manifold is hyperbolic if its holomorphic sectional curvature is bounded above by -1.

• 대한수학회논문집
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• 제21권1호
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• pp.177-183
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• 2006

The purpose of this paper is to introduce an L-metrical non-linear connection $N_j^{*i}$ and investigate a conformal change in the Finsler space with $({\alpha},\;{\beta})-metric$. The (v)h-torsion and (v)hvtorsion in the Finsler space with L-metrical connection $F{\Gamma}^*$ are obtained. The conformal invariant connection and conformal invariant curvature are found in the above Finsler space.

• 대한수학회논문집
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• 제17권3호
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• pp.505-517
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• 2002

We introduce certain conformally invariant h-Finsler connection in a Rizza manifold. Using this connection, we find some conformally invariant Finsler tensors. The conformal flatness and the Kaehlerian Finsler manifold with respect to the above connection are investigated.

• 대한수학회지
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• 제37권1호
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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.

• 대한수학회지
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• 제55권2호
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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.

• 대한수학회보
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• 제36권2호
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• pp.217-224
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• 1999

In this paper the properties of the Finsler metrics compatible with an f-structure are investigated.

• 대한수학회보
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• 제43권2호
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• pp.425-441
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• 2006

We have two concepts of Douglas spaces and Lands-berg spaces as generalizations of Berwald spaces. S. Bacso gave the definition of a weakly-Berwald space [2] as another generalization of Berwald spaces. In the present paper, we find the conditions that the Finsler space with an (${\alpha},{\beta}$)-metric be a weakly-Berwald space and the Finsler spaces with some special (${\alpha},{\beta}$)-metrics be weakly-Berwald spaces, respectively.