• 대한수학회지
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• 제54권3호
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• pp.793-805
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• 2017

In this paper, we prove that the Ricci tensor of a three-dimensional almost Kenmotsu manifold satisfying ${\nabla}_{\xi}h=0$, $h{\neq}0$, is ${\eta}$-parallel if and only if the manifold is locally isometric to either the Riemannian product $\mathbb{H}^2(-4){\times}\mathbb{R}$ or a non-unimodular Lie group equipped with a left invariant non-Kenmotsu almost Kenmotsu structure.

• 대한수학회논문집
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• 제11권4호
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• pp.1077-1085
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• 1996

This paper provides examples which can not be approximate fibrations and shows that if $N^n$ is a closed aspherical manifold, $\pi_1(N)$ is hyperhophian, normally cohophian, and $\pi_1(N)$ has no nontrivial Abelian normal subgroup, then the product of $N^n$ and a sphre $S^m$ satisfies the property that all PL maps from an orientable manifold M to a polyhedron B for which each point preimage is homotopy equivalent to $N^n \times S^m$ necessarily are approximate fibrations.

• 대한수학회보
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• 제55권3호
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• pp.789-798
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• 2018

Let M be a compact almost $coK{\ddot{a}}hler$ 5-manifold with $K{\ddot{a}}hlerian$ leaves. In this paper, we prove that M is locally symmetric if and only if it is locally isometric to a Riemannian product of a unit circle $S^1$ and a locally symmetric compact $K{\ddot{a}}hler$ 4-manifold.

• 대한수학회보
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• 제38권2호
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• pp.223-230
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• 2001

In this parper, we considered the uniqueness of positive time-solution to equation ${\Box}_g$u(t,$\chi$) - $c_n$u(t,$\chi$) + $c_n$u(t,$\chi$)$^[\frac{n+3}{n-3}]$ = 0, where $c_n$ = $\frac{n-1}{4n}$ and ${\Box}_g$ is the d'Alembertian for a Lorentzian warped manifold M = {a,$\infty$] $\times_f$ N.

• 한국CDE학회논문집
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• 제4권2호
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• pp.121-126
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• 1999

Existing data structures for non-manifold solid modelers use basic dat entities, such as vertex, edge, loop, face, shell, and region to find adjacency relationships. But, no one clearly identified what additional types of data entitles are necessary to represent incidence relationships. In this paper, we classified the boundary information of vertex, edge, face , and region from the 3-D space view. As the results we can clearly define the boundary information required for adjacency relationships. The existing B-rep data structures for solid modeler are compared whether they have the required boundary information.

• 대한수학회논문집
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• 제35권4호
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• pp.1245-1254
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• 2020

The object of the present paper is to characterize Bach flat (k, 𝜇)-almost co-Kähler manifolds. It is proved that a Bach flat (k, 𝜇)-almost co-Kähler manifold is K-almost co-Kähler manifold under certain restriction on 𝜇 and k. We also characterize (k, 𝜇)-almost co-Kähler manifolds with divergence free Cotton tensor.

• 대한수학회논문집
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• 제35권4호
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• pp.1255-1267
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• 2020

The class of isotropic almost complex structures, J_𝛿,𝜎, define a class of Riemannian metrics, g_𝛿,𝜎, on the tangent bundle of a Riemannian manifold which are a generalization of the Sasaki metric. This paper characterizes the metrics g_𝛿,0 using the geometry of tangent bundle. As a by-product, some integrability results will be reported for J_𝛿,𝜎.

• 대한수학회논문집
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• 제33권4호
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• pp.1331-1339
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• 2018

In this paper the decomposition of basic equations of $(LCS)_n$-manifolds is carried out into horizontal and vertical projections. Further, we study the integrability of the distributions $D,D{\oplus}[{\xi}]$ and $D^{\perp}$ totally geodesic of semi-invariant submanifolds of $(LCS)_n$-manifold.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권3호
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• pp.199-206
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• 2013

We present a 4-dimensional nil-manifold as the first example of a closed non-K$\ddot{a}$hlerian symplectic manifold with the following property: a function is the scalar curvature of some almost K$\ddot{a}$hler metric iff it is negative somewhere. This is motivated by the Kazdan-Warner's work on classifying smooth closed manifolds according to the possible scalar curvature functions.

• 대한수학회논문집
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• 제16권4호
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• pp.637-648
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• 2001

An n-dimensional ME-manifold ME $X_{n}$ is a general-ized Riemannian manifold connected by the ME-connection which is both Einstein and of the form (2.13). The purpose of this paper is to study the properties of the ME-curvature tensors, the con-tracted ME-curvature tensors and the field equations in ME $X_{n}$)n)