• Honam Mathematical Journal
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• v.25 no.1
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• pp.163-172
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• 2003

In this paper we study the property of harmonic vector fields. We call a vector fields ${\xi}$ harmonic if it is a harmonic map from the manifold into its tangent bundle with the Sasaki metric. We show that the characteristic polynomial of operator $A={\nabla}{\xi}\;in\;S^{2n+1}\;is\;(x^2+1)^n$.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1321-1336
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• 2018

In this paper, we obtain some necessary and sufficient conditions for the Reeb vector field of a trans-Sasakian 3-manifold to be minimal or harmonic. We construct some examples to illustrate main results. As applications of the above results, we obtain some new characteristic conditions under which a compact trans-Sasakian 3-manifold is homothetic to either a Sasakian or cosymplectic 3-manifold.

• Korean Journal of Mathematics
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• v.31 no.2
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• pp.139-144
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• 2023

In this paper, we show that a recurrent manifold with harmonic curvature tensor is locally symmetric and that an Einstein and conformally recurrent manifold is locally symmetric. As a consequence, Einstein and recurrent manifolds must be locally symmetric. On the other hand, we have obtained some results for a (conformally) recurrent manifold with parallel vector field and also investigated some results for a (conformally) recurrent manifold with concircular vector field.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.73-80
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• 1992

We discuss transverse harmonic fields on compact foliated Riemannian manifolds, and give a necessary and sufficient condition for a transverse field to be a transverse harmonic one and the non-existence of transverse harmonic fields. 1. On a foliated Riemannian manifold, geometric transverse fields, that is, transverse Killing, affine, projective, conformal fields were discussed by Kamber and Tondeur([3]), Molino ([5], [6]), Pak and Yorozu ([7]) and others. If the foliation is one by points, then transverse fields are usual fields on Riemannian manifolds. Thus it is natural to extend well known results concerning those fields on Riemannian manifolds to foliated cases. On the other hand, the following theorem is well known ([1], [10]): If the Ricci operator in a compact Riemannian manifold M is non-negative everywhere, then a harmonic vector field in M has a vanishing covariant derivative. If the Ricci operator in M is positive-definite, then a harmonic vector field other than zero does not exist in M.

• Journal of the Optical Society of Korea
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• v.20 no.1
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• pp.135-139
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• 2016

I propose a vector passive harmonic mode-locked fiber laser based on topological insulator Bi2Se3 interacting with a fiber taper with a diameter of 7 μm. The particles of topological insulator are deposited uniformly onto the fiber taper with light pressure effect. By incorporating the fabricated saturable absorber into an Er-doped fiber laser cavity, stable mode-locked fiber is obtained. Due to the intense evanescent field of the fiber taper, strong confinement of light enhances the nonlinearity of the laser cavity, and passive harmonic mode-locking is performed. I observe a maximum harmonic mode-locking of 356th, corresponding to a frequency of 3.57 GHz. The pulse duration is 824 fs, and the full width at half maximum of the spectrum is about 8.2 nm. The polarization dependent loss of the saturable absorber is ~ 2.5 dB in the wavelength range of the C band. As the cavity contains no other polarization dependent device, the mode-locked laser is functioning in the vector state. The harmonic order vs pump power is investigated. To the best of our knowledge, this report is the highest frequency mode-locked fiber laser based on Bi2Se3. Experimental results indicate that the topological insulator Bi2Se3 functioning with a thin fiber taper is effective for vector harmonic mode-locking.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.1019-1035
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• 2020

In this paper, we introduce the deformed-Sasaki metric on the tangent bundle TM over an m-dimensional Riemannian manifold (M, g), as a new natural metric on TM. We establish a necessary and sufficient conditions under which a vector field is harmonic with respect to the deformed-Sasaki Metric. We also construct some examples of harmonic vector fields.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.51 no.11
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• pp.616-621
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• 2002

With biological effects by ELF (Extremely Low Frequency) magnetic field generated from power system, the transient magnetic field from electric appliances is a major issue presently. Because the transient magnetic field induces higher current than the power frequency field inside living bodies, transient magnetic field exposure has been much focused. In this paper, it is shown that transient magnetic field from electric home appliances can be characterized as magnetic dipole moment. In this method, the dipole moment vector is assumed by allowing an uncertainty of 6dB in the estimated field. A parameter M that represents biological interaction was applied also. The proposed method was applied to 7 types of appliances (hair drier, heater, VDT, etc.) and their equivalent magnetic dipole moment and harmonic components were estimated. As the results, the useful data for quantifying magnetic field distribution around electric appliances were obtained.

• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.169-179
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• 2021

In this paper, we extend the definition of p-harmonic maps between two Riemannian manifolds. We prove a Liouville type theorem for generalized p-harmonic maps. We present some new properties for the generalized stress p-energy tensor. We also prove that every generalized p-harmonic map from a complete Riemannian manifold into a Riemannian manifold admitting a homothetic vector field satisfying some condition is constant.

• 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.59 no.1
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• pp.101-110
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• 2022

In this article, the notion of *-conformal Ricci soliton is defined as a self similar solution of the *-conformal Ricci flow. A Sasakian 3-metric satisfying the *-conformal Ricci soliton is completely classified under certain conditions on the soliton vector field. We establish a relation with Fano manifolds and proves a homothety between the Sasakian 3-metric and the Berger Sphere. Also, the potential vector field V is a harmonic infinitesimal automorphism of the contact metric structure.