• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.231-240
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• 2005

The paper shows that a hypersurface with constant curvature with the condition $hD{\subset}D$, of a contact metric manifold with a nullity condition and ${\varphi}-constant$ sectional curvature, has the curvature equals to k and ${\mu}=0$.

• Honam Mathematical Journal
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• v.27 no.2
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• pp.267-271
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• 2005

We study hypersurfaces in the Euclidean space with the following property: the tangential part of the position vector has constant length. As a result, we prove that among the connected and complete hypersurfaces in the Euclidean space, only the hypersphere centered at the origin satisfies the property.

• Honam Mathematical Journal
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• v.28 no.1
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• pp.83-111
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• 2006

After introducing Tropical Algebraic Varieties, we give a polyhedral description of tropical hypersurfaces. Using TOPCOM and GAP, we show that there exist 59 types of two dimensional tropical quadric surfaces. We also show a criterion for a quadric hypersurface to be non-degenerate in terms of a tropical rank.

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.417-423
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• 2006

The object of the present paper is to study a conformally flat quasi-Einstein space and its hypersurface.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.335-342
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• 2011

In this paper, we prove that minimal hypersurfaces when n $\geq$ 3 and nonzero constant mean curvature hypersurfaces when n $\geq$ 2 foliated by spheres in parallel horizontal hyperplanes in $\mathbb{H}^n{\times}\mathbb{R}$ must be rotationally symmetric.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1771-1783
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• 2016

We study lightlike hypersurfaces M of an indefinite trans-Sasakian manifold ${\bar{M}}$ with a non-metric ${\phi}$-symmetric connection. We characterize the geometry of lightlike hypersurfaces of such a ${\bar{M}}$.

• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.411-417
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• 2007

N(k)-quasi Einstein manifolds are introduced and studied.

• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.419-428
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• 2007

In this paper, we will investigate the Hessian geometry of the homogeneous domain over the hypersurface given by a function F : $\mathbb{R}^n{\rightarrow}\mathbb{R}$ with ${\mid}{\det}\;DdF\mid=1$.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.353-360
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• 2013

We study lightlike hypersurfaces of indefinite Kenmotsu manifolds. The purpose of this paper is to prove that there do not exist totally geodesic screen distributions on semi-symmetric lightlike hypersurfaces of indefinite Kenmotsu manifolds with flat transversal connection.

• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.341-353
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• 2010

In this paper, we study the geometry of screen conformal lightlike real hypersurfaces of an indefinite Kaehler manifold. The main result is a characterization theorem for screen conformal lightlike real hypersurfaces of an indefinite complex space form.