• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.183-200
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• 2012

In the present paper, we consider the condition that is a geodesic equation on a Finsler space with an (${\alpha},\;{\beta}$)-metric. Next we find the conditions that are equations of geodesic on the Finsler space with an approximate infinite series (${\alpha},\;{\beta}$)-metric.

• Journal of applied mathematics & informatics
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• v.41 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.1011-1018
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• 2022

In this work, magnetic geodesics over the space of Kähler potentials are studied through a variational method for a generalized Landau-Hall functional. The magnetic geodesic equation is calculated in this setting and its relation to a perturbed complex Monge-Ampère equation is given. Lastly, the magnetic geodesic equation is considered over the special case of toric Kähler potentials over toric Kähler manifolds.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1459-1468
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• 2018

We show that an umbilic-free minimal surface in ${\mathbb{R}}^3$ belongs to the associate family of the catenoid if and only if the geodesic curvatures of its lines of curvature have a constant ratio. As a corollary, the helicoid is shown to be the unique umbilic-free minimal surface whose lines of curvature have the same geodesic curvature. A similar characterization of the deformation family of minimal surfaces with planar lines of curvature is also given.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.337-346
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• 2000

The geodesic equation in a two-dimensional Finsler space is given by the differential equation of the Weierstrass form. In the present paper, we express the differential equations of geodesics in a two-dimensional Finsler space with a generalized Kropina metric.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.331-340
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• 2018

Using the comparison of differential equations involving Ricci and scalar curvatures obtained by Eschenburg and O'Sullivan, the scalar curvatures of level hypersurfaces of geodesic spheres are compared.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.767-775
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• 2010

Let ${\varphi}\;:\;(M^n,\;F)\;{\rightarrow}\;(\overline{M}^{n+p},\;\overline{F})$ be an isometric immersion from a Finsler manifold to a Finsler manifold. In this paper, we shall obtain the Gauss and Codazzi equations with respect to the Chern connection on submanifolds M, by which we prove that if M is a weakly totally geodesic submanifold of $\overline{M}$, then flag curvature of M equals flag curvature of $\overline{M}$.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.279-293
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• 2002

In this paper, we prove that if every totally real bisectional curvature of an n($\geq$3)-dimensional complete Kahler submanifold of a complex projective space of constant holomorphic sectional curvature c is greater than (equation omitted) (3n$^2$+2n-2), then it is totally geodesic and compact.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2000.04a
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• pp.211-214
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• 2000

Filament wound pressure vessels have been studied for the efficient design tool to consider the variation of fiber angles through-the thickness direction. Filament winding patterns were simulated from semi-geodesic fiber path equation to calculate fiber path on arbitrary surface. Finite element analyses were performed considering fiber angle variation in longitudinal and thickness directions by ABAQUS. For the finite element modeling of the pressure tank, the 3-dimensional layered solid element was utilized. From the stress results of pressure tanks, maximum stress criterion in transverse direction was applied to modify material properties for failed region. In the end of each load increment, resultant layer stresses were compared with a failure criterion and properties were reduced to 1/10 for a failed layer. Results of progressive failure analysis were compared with two experimental data.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.363-368
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• 2018

The aim of this work is to derive a partial differential equation that explains the movement of vortex lines on a vortex trajectory surface in a three dimensional incompressible inviscid flow.