• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.1-16
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• 2018

In this paper, we give characteristic differential equations of a kind of projective vector fields on Finsler manifolds. Using these equations, we prove the vanishing theorem of projective vector fields on any compact Finsler manifold with the negative mean Ricci curvature, which is defined in [10]. This result involves the vanishing theorem of Killing vector fields in the Riemannian case and the work of [1, 14].

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1505-1521
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• 2008

In this paper, we give a characterization of the structurally stable vector fields via the notion of orbital inverse shadowing. More precisely, it is proved that the $C^1$ interior of the set of $C^1$ vector fields with the orbital inverse shadowing property coincides with the set of structurally stable vector fields. This fact improves the main result obtained by K. Moriyasu et al. in [15].

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.605-613
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• 2007

Main interest of the present paper is to investigate the criticality of characteristic vector fields on almost cosymplectic manifolds. Killing critical characteristic vector fields are absolute minima. This paper contains some examples of non-Killing critical characteristic vector fields.

• Bulletin of the Korean Mathematical Society
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• v.46 no.4
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• pp.713-720
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• 2009

We find all left-invariant minimal unit vector fields and strongly normal unit vector fields on a Lie group which is isometric to the hyperbolic space.

• Honam Mathematical Journal
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• v.45 no.2
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• pp.300-315
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• 2023

In this article, we deal with the biharmonicity of a vector field X viewed as a map from a pseudo-Riemannian manifold (M, g) into its tangent bundle TM endowed with the Sasaki metric g_S. Precisely, we characterize those vector fields which are biharmonic maps, and find the relationship between them and biharmonic vector fields. Afterwards, we study the biharmonicity of left-invariant vector fields on the three dimensional Heisenberg group endowed with a left-invariant Lorentzian metric. Finally, we give examples of vector fields which are proper biharmonic maps on the Gödel universe.

• Journal of the Korean Vacuum Society
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• v.21 no.2
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• pp.69-77
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• 2012

Visualization of the electromagnetic vector fields are presented and examined with Mathematica. Vector fields may be used to represent a great of many physical quantities in various area of physics, including electromagnetism with vector differential operators. Because they deal with abstract, three-dimensional fields that are some times very difficult to visualize, electromagnetism can be conceptually rather difficult. Visual representation of such an abstract vector fields is invaluable to student or researchers working in this field and also helps teaching electromagnetism to physics or engineering students. Mathematica provides a wider range of graphical tools including plot of vector fields and vector analysis, which can be applied to visualization of electromagnetic system. We have visualized the most fundamental concepts of the electromagnetic vector $\vec{E}=-\vec{\nabla}_{\varphi}$, $\vec{D}={\epsilon}\vec{E}$, $\vec{\nabla}{\times}\vec{A}$, $\vec{B}={\mu}\vec{H}$, $\vec{B}={\mu}_0(\vec{H}+\vec{M})$, which are confirmed with vector calculations and valid graphically with some presentations.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.133-145
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• 2006

We study Riemannian or pseudo-Riemannian manifolds which admit a closed conformal vector field. Subject to the condition that at each point $p{\in}M^n$ the set of conformal gradient vector fields spans a non-degenerate subspace of TpM, using a warped product structure theorem we give a complete description of the space of conformal vector fields on arbitrary non-Ricci flat Einstein spaces.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.121-129
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• 2010

Using a degree theory for countably condensing multivalued maps, we show that under certain conditions an invariance of domain theorem holds for countably condensing or countably k-contractive multivalued vector fields.

• The Mathematical Education
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• v.29 no.1
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• pp.63-68
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• 1990

Let M be a differentiable manifold, TM its tangent bundle and FM its frame bundle. The theory of complete lifts and Horizontal lifts to FM of vector fields on M ahs been studied by many authors. Tn this paper, vertical lifts of functions vector fields md 1-forms on M to FM are studied.

• Proceedings of the KIEE Conference
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• 1997.07b
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• pp.422-424
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• 1997

In this paper, we characterize the whole class of vector fields that can be linearized by a given nominal state transformation and a feedback linearizing controller. The necessary and sufficient condition for a given uncertain vector field to be so-called "completely linearizable by the nominal coordinate transformation" is given in terms of Lie Bracket of uncertain vector fields and some suitable vector fields of the nominal system.