• 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.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.429-442
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• 2017

In the present paper, screen isotropic leaves on lightlike hypersurfaces of a Lorentzian manifold are introduced and studied which are inspired by the definition of isotropic immersions in the Riemannian context. Some examples of such leaves are mentioned. Furthermore, some relations involving curvature invariants are obtained.

• East Asian mathematical journal
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• v.30 no.5
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• pp.599-607
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• 2014

We study lightlike hypersurfaces M of an indefinite Kaehler manifold $\bar{M}$ of quasi-constant curvature subject to the condition that the curvature vector field of $\bar{M}$ belongs to the screen distribution S(TM). We provide several new results on such lightlike hypersurfaces M.