• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.859-893
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• 2009

In this article, we will characterize structures of geometric quotient orbifolds of G-manifold of genus two where G is a finite group of orientation preserving diffeomorphisms using the idea of handlebody orbifolds. By using the characterization, we will deduce the candidates of possible non-hyperbolic geometric quotient orbifolds case by case using W. Dunbar's work. In addition, if the G-manifold is compact, closed and the quotient orbifold's geometry is hyperbolic then we can show that the fundamental group of the quotient orbifold cannot be in the class D.

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.733-740
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• 2015

In this paper, we prove the existence of warping functions on Riemannian warped product manifolds with some prescribed scalar curvatures according to the fiber manifolds of class (B).

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.829-836
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• 2005

In this note, we introduce a new proof of the unique-ness and existence of a negatively bounded solution for a parabolic partial differential equation. The uniqueness in particular implies the finiteness of the Fourier spanning dimension of the global attractor and the existence allows a construction of an inertial manifold.

• 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.29 no.4
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• pp.539-547
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• 2014

In this paper, we study two types 1-lightlike submanifolds M, so called lightlike hypersurface and half lightlike submanifold, of an indefinite Kaehler manifold $\bar{M}$ admitting non-metric ${\pi}$-connection. We prove that there exist no such two types 1-lightlike submanifolds of an indefinite Kaehler manifold $\bar{M}$ admitting non-metric ${\pi}$-connections.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.443-457
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• 2012

In this paper, we introduce screen slant lightlike submanifold of an indefinite Sasakian manifold and give examples. We prove a characterization theorem for the existence of screen slant lightlike submanifolds. We also obtain integrability conditions of both screen and radical distributions, prove characterization theorems on the existence of minimal screen slant lightlike submanifolds and give an example of proper minimal screen slant lightlike submanifolds of $R_2^9$.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.677-683
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• 2008

On a compact n-dimensional manifold M, it has been conjectured that a critical point metric of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of volume 1, should be Einstein. The purpose of the present paper is to prove that a 3-dimensional manifold (M,g) is isometric to a standard sphere if ker $s^*_g{{\neq}}0$ and there is a lower Ricci curvature bound. We also study the structure of a compact oriented stable minimal surface in M.

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.121-136
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• 1996

Met $\tilde{M} = (\tilde{M}, \tilde{J}, <>)$ be an almost Hermitian manifold and M a submanifold of $\tilde{M}$. According to the behavior of the tangent bundle TM with respect to the action of $\tilde{J}$, we have two typical classes of submanifolds. One of them is the class of almost complex submanifolds and another is the class of totally real submanifolds. In 1990, B. Y. Chen [4], [5] introduced the concept of the class of slant submanifolds which involve the above two classes. He used the Wirtinger angle to measure the behavior of TM with respect to the action of $\tilde{J}$.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.841-846
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• 2006

Suppose that F is a closed t-aspherical PL n-manifold with finite, sparsely abelian ${\pi}_1(F)$ and A is a closed aspherical PL m-manifold with hopfian, normally cohopfian ${\pi}_1(A)$. If $X(F){\neq}0{\neq}X(A)$, then $F{\times}A$ is a codimension-(t+1) PL fibrator.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.789-799
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• 2009

In this study we consider ${\varphi}$-conformally flat, ${\varphi}$-conharmonically flat, ${\varphi}$-projectively at and ${\varphi}$-concircularly flat Lorentzian ${\alpha}$-Sasakian manifolds. In all cases, we get the manifold will be an ${\eta}$-Einstein manifold.