• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.471-484
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• 2005

We study Riemannian or pseudo-Riemannian manifolds which carry the space of closed conformal vector fields of at least 2-dimension. Subject to the condition that at each point the set of closed conformal vector fields spans a non-degenerate subspace of the tangent space at the point, we prove a global and a local classification theorems for such manifolds.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.523-537
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• 2020

In this work we consider the Sol₃ Lie group, equipped with the left-invariant metric, Lorentzian or Riemannian. We determine Killing vector fields and affine vectors fields. Also we obtain a full classification of Ricci, curvature and matter collineations.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.1005-1018
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• 2020

A characterization of the C-projective vector fields on a Randers space is presented in terms of 𝚵-curvature. It is proved that the 𝚵-curvature is invariant for C-projective vector fields. The dimension of the algebra of the C-projective vector fields on an n-dimensional Randers space is at most n(n + 2). The generalized Funk metrics on the n-dimensional Euclidean unit ball 𝔹ⁿ(1) are shown to be explicit examples of the Randers metrics with a C-projective algebra of maximum dimension n(n+2). Then, it is also proved that an n-dimensional Randers space has a C-projective algebra of maximum dimension n(n + 2) if and only if it is locally Minkowskian or (up to re-scaling) locally isometric to the generalized Funk metric. A new projective invariant is also introduced.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.67-76
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• 2014

Let X be a divergence-free vector field defined on a closed, connected Riemannian manifold. In this paper, we show the equivalence between the following conditions: ${\bullet}$ X is a divergence-free vector field satisfying the shadowing property. ${\bullet}$ X is a divergence-free vector field satisfying the Lipschitz shadowing property. ${\bullet}$ X is an expansive divergence-free vector field. ${\bullet}$ X has no singularities and is Anosov.

• 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 $A={\nabla}{\xi}\;in\;S^{2n+1}\;is\;(x^2+1)^n$.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1339-1350
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• 2018

We will find a necessary and sufficient condition for unit Killing vector fields to be minimal and provide an application of the obtained result.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.425-434
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• 2021

The object of the present paper is to deduce some important results on generic submanifolds and generic product of trans-Sasakian manifolds with concurrent vector fields.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.78-87
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• 2021

In this study, we firstly compute the energies and the angles of Frenet vector fields in Lorentz 5-space ��5. Then we obtain the bienergies and biangels of Frenet vector fields in ��5 by using the values of energies and angles. Finally, we present the relations among energies, angles, bienergies, and biangles with graphics.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.361-375
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• 2021

The object of the present paper is to deduce some important results on generic submanifolds and also generic product of LP-Sasakian manifolds with concurrent vector fields. Also, we provide a necessary and sufficient condition for which the invariant distribution D and anti-invariant distribution D^⊥ of M are Einstein. Also, we deduce an interesting necessary and sufficient condition for submanifolds of LP-Sasakian manifolds to be totally umbilical submanifolds. Especially we deal with the generic submanifolds admitting a Ricci soliton in LP-Sasakian manifolds endowed with concurrent vector fields.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1443-1482
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• 2008

In this paper we define a Myller configuration in a Finsler space and use some special configurations to obtain results about Finsler subspaces. Let $F^{n}$ = (M,F) be a Finsler space, with M a real, differentiable manifold of dimension n. Using the pull back bundle $({\pi}^{*}TM,\tilde{\pi},\widetilde{TM})$ of the tangent bundle $(TM,{\pi},M)$ by the mapping $\tilde{\pi}={\pi}/TM$ and the Cartan Finsler connection of a Finsler space, we obtain an orthonormal frame of sections of ${\pi}^{*}TM$ along a regular curve in $\widetilde{TM}$ and a system of invariants, geometrically associated to the Myller configuration. The fundamental equations are written in a very simple form and we prove a fundamental theorem. Important lines in a Finsler subspace are defined like special lines in a Myller configuration, geometrically associated to the subspace: auto parallels, lines of curvature, asymptotes. Torse forming vector fields with respect to the Cartan Finsler connection are characterized by means of the invariants of the Frenet frame of a versor field along a curve, and the new notion of torse forming vector fields in the sense of Myller is introduced. The particular cases of concurrence and parallelism in the sense of Myller are completely studied, for vector fields from the distribution $T^m$ of the Myller configuration and also from the normal distribution $T^p$.