• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.243-252
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• 2001

The purpose of this paper is to study some properties of n-dimensional recurrent space-like complex hypersurfaces in an (n+1)-dimensional semi-definite complex space form M(sub)0+t(sup)n+1 (c), t = 0 or 1, c$\neq$0.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1631-1647
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• 2015

In this paper, we prove two optimal inequalities involving the intrinsic scalar curvature and extrinsic Casorati curvature of submanifolds of generalized space forms endowed with a semi-symmetric metric connection. Moreover, we also characterize those submanifolds for which the equality cases hold.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.331-343
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• 2014

The object of the present paper is to study a semi-symmetric metric connection in an (${\varepsilon}$)-Kenmotsu manifold. In this paper, we study a semi-symmetric metric connection in an (${\varepsilon}$)-Kenmotsu manifold whose projective curvature tensor satisfies certain curvature conditions.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.609-618
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• 2004

Pseudo-parallel real hypersurfaces in complex space forms can be defined as an extrinsic analogues of pseudo-symmetric real hypersurfaces, that generalize the notion of semi-symmetric real hypersurface. In this paper a classification of the pseudo-parallel real hypersurfaces in a non-flat complex space forms is obtained.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.1047-1065
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• 2017

The notion of a non-metric ${\phi}$-symmetric connection on semi-Riemannian manifolds was introduced by Jin [6, 7]. The object of study in this paper is generic lightlike submanifolds of an indefinite Kaehler manifold ${\bar{M}}$ with a non-metric ${\phi}$-symmetric connection. First, we provide several new results for such generic lightlike submanifolds. Next, we investigate generic lightlike submanifolds of an indefinite complex space form ${\bar{M}}(c)$ with a non-metric ${\phi}$-symmetric connection.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.179-193
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• 2023

In this article, we derived Chen's inequality for warped product bi-slant submanifolds in generalized complex space forms using semisymmetric metric connections and discuss the equality case of the inequality. Further, we discuss non-existence of such minimal immersion. We also provide various applications of the obtained inequalities.

• 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.

• 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.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.665-678
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• 2014

We present a new space-time discontinuous Galerkin (DG) method for solving the time dependent, positive symmetric hyperbolic systems. The main feature of this DG method is that the discrete equations can be solved semi-explicitly, layer by layer, in time direction. For the partition made of triangle or rectangular meshes, we give the stability analysis of this DG method and derive the optimal error estimates in the DG-norm which is stronger than the $L_2$-norm. As application, the wave equation is considered and some numerical experiments are provided to illustrate the validity of this DG method.