• 대한수학회지
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• 제40권6호
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• pp.951-962
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• 2003

In this paper we address focal points and treat manifolds (M, g) whose Lorentzian metric tensors g have a spacelike $C^{0}$-hypersurface $\Sigma$ [10]. We apply Jacobi fields for such manifolds, and check the local length maximizing properties of $C^1$-geodesics. The condition of maximality of timelike curves(geodesics) passing $C^{0}$-hypersurface is studied.ied.

• 대한수학회논문집
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• 제29권4호
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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.

• 대한수학회보
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• 제50권4호
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• pp.1367-1376
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• 2013

We study Einstein lightlike hypersurfaces M of a Lorentzian space form $\tilde{M}(c)$ admitting a semi-symmetric non-metric connection subject to the conditions; (1) M is screen conformal and (2) the structure vector field ${\zeta}$ of $\tilde{M}$ belongs to the screen distribution S(TM). The main result is a characterization theorem for such a lightlike hypersurface.

• 대한수학회논문집
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• 제17권2호
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• pp.261-278
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• 2002

Let G = O(2) $\times$ O(2) $\times$O(2) and let M$^4$be closed G-invariant minimal hypersurface with constant scalar curvature in S$^{5}$ . If M$^4$has 2 distinct principal curvatures at some point, then S = 4. Moreover, if S > 4, then M$^4$does not have simple principal curvatures everywhere.

• 대한수학회논문집
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• 제11권3호
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• pp.757-766
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• 1996

The purpose of this paper is to study a real hypersurface of $M_n(c)$ where structure vector $\zeta$ is principal and satisfying $\bigtriangledown_\zeta S = (\bigtriangledown S)\zeta$ (section 2) and also satisfying $\bigtriangledown_\zeta S = a(S \phi - \phi S)$ (section 3) where a is constant.

• 호남수학학술지
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• 제30권4호
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• pp.743-748
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• 2008

In this article, we study ruled hypersurfaces in a Lorentz-Minkowski space which has finite type immersion. As a result, we give a complete classification of ruled hypersurfaces or finite type immersion into a Lorentz-Minkowski space ${\mathbb{L}}^m$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권4호
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• pp.229-236
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• 2014

In this paper, we study two types of 1-lightlike submanifolds, named by lightlike hypersurface and half lightlike submanifold, of an indefinite Sasakian manifold admitting non-metric ${\theta}$-connections. We prove that there exist no such two types of 1-lightlike submanifolds of an indefinite Sasakian manifold.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권3호
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• pp.197-206
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• 2004

We obtain some characterizations of a pseudo Ricci-parallel real hypersurface in a quaternionic projective space $QP^{n}$ and find the condition that M is locally congruent to a geodesic hypersphere of $QP^{n}$ .

• 대한수학회보
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• 제42권2호
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• pp.279-294
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• 2005

We study a real hypersurface M satisfying $L_{\xi}S=0\;and\;R_{\xi}S=SR_{\xi}$ in a complex hyperbolic space $H_n\mathbb{C}$, where S is the Ricci tensor of type (1,1) on M, $L_{\xi}\;and\;R_{\xi}$ denotes the operator of the Lie derivative and the Jacobi operator with respect to the structure vector field e respectively.

• 대한수학회논문집
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• 제18권1호
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• pp.75-85
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• 2003

Let M be 3 Semi-invariant submanifold of codimension 3 with lift-flat normal connection in a complex projective space. Further, if the mean curvature of M is constant, then we prove that M is a real hypersurface of a complex projective space of codimension 2 in the ambient space.