• 대한수학회보
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• 제50권3호
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• pp.705-717
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• 2013

In this paper, we study the geometry of half lightlike submanifolds M of a semi-Riemannian manifold $\tilde{M}$ with a semi-symmetric non-metric connection subject to the conditions; (1) the characteristic vector field of $\tilde{M}$ is tangent to M, the screen distribution on M is totally umbilical in M and the co-screen distribution on M is conformal Killing, or (2) the screen distribution is integrable and the local lightlike second fundamental form of M is parallel.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권1호
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• pp.51-61
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• 2011

In this paper, we study the geometry of transversal half lightlike sub-manifolds of an indefinite Sasakian manifold. The main result is to prove three characterization theorems for such a transversal half lightlike submanifold. In addition to these main theorems, we study the geometry of totally umbilical transversal half lightlike submanifolds of an indefinite Sasakian manifold.

• 대한수학회논문집
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• 제33권1호
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• pp.305-315
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• 2018

This note provides a study of lightlike hypersurfaces of a generalized Robertson-Walker(GRW) space-time with a certain screen distribution, which are integrable and have good properties. Focus is to investigate geometric features from the relation of the second fundamental forms between lightlike hypersurfaces and leaves of the integrable screen distribution. Also, we shall apply those results on lightlike hypersurfaces of a GRW space-time to lightlike hypersurfaces of a Robertson-Walker(RW) space-time.

• 대한수학회논문집
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• 제38권1호
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• pp.223-234
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• 2023

The main purpose of this paper is to study the lightlike hypersurface (M, $\overline{g}$) of cosymplectic space form $\overline{M}$(c). In this paper, we computed the Gauss and Codazzi formulae of (M, $\overline{g}$) of cosymplectic manifold ($\overline{M}$, g). We showed that we can't obtain screen semi-invariant lightlike hypersurface (SCI-LH) of $\overline{M}$(c) with parallel second fundamental form h, parallel screen distribution and c ≠ 0. We showed that if second fundamental form h and local second fundamental form B are parallel, then (M, $\overline{g}$) is totally geodesic. Finally we showed that if (M, $\overline{g}$) is umbilical, then cosymplectic manifold ($\overline{M}$, g) is flat.

• Kyungpook Mathematical Journal
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• 제60권2호
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• pp.223-238
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• 2020

We study a lightlike hypersurface M of an indefinite nearly trans-Sasakian manifold ${\bar{M}}$ with an (ℓ, m)-type connection such that the structure vector field ζ of ${\bar{M}}$ is tangent to M. In particular, we focus on such lightlike hypersurfaces M for which the structure tensor field F is either recurrent or Lie recurrent, or such that M itself is totally umbilical or screen totally umbilical.

• 대한수학회논문집
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• 제27권1호
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• pp.185-195
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• 2012

We study the geometry of lightlike hypersurfaces M of an inde nite cosymplectic manifold $\bar{M}$ such that either (1) the characterist vector field $\zeta$ of $\bar{M}$ belongs to the screen distribution S(TM) of M or (2) $\zeta$ belongs to the orthogonal complement $S(TM)^{\perp}$ of S(TM) in $T\bar{M}$.

• 대한수학회논문집
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• 제29권1호
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• pp.109-121
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• 2014

In this paper, we study the geometry of half lightlike submanifolds of an indefinite Sasakian manifold. There are several different types of half lightlike submanifolds of an indefinite Sasakian manifold according to the form of its structure vector field. We study two types of them here: tangential and ascreen half lightlike submanifolds.