• Communications of the Korean Mathematical Society
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• v.33 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.30 no.2
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• pp.109-121
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• 2015

In this paper, we investigate horizontal lightlike hypersurfaces of Robertson-Walker spacetimes. Some results involving the unique existence of the screen distribution and the symmetry of the induced Ricci curvature tensor of horizontal lightlike hypersurfaces are presented. We also obtain some properties concerning the symmetry and the parallelism of the second fundamental forms of such lightlike hypersurfaces.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.101-115
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• 2017

In this paper, we study three types of lightlike hypersurfaces, which are called recurrent, Lie recurrent and Hopf lightlike hypersurfaces, of an indefinite Kaehler manifold with a semi-symmetric non-metric connection. We provide several new results on such three types of lightlike hypersurfaces of an indefinite Kaehler manifold or an indefinite complex space form, with a semi-symmetric non-metric connection.

• 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.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.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.409-416
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• 2009

In this paper, we study the geometry of lightlike hypersurfaces of a semi-Riemannian manifold. We prove a classification theorem for lightlike hypersurfaces M with totally umbilical screen distributions of a semi-Riemannian space form.

• The Pure and Applied Mathematics
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• v.20 no.1
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• pp.25-35
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• 2013

In this paper, we study lightlike hypersurfaces of an indefinite Sasakian manifold $\bar{M}$. First, we construct a type of lightlike hypersurface according to the form of the structure vector field of $\bar{M}$, named by ascreen lightlike hypersurface. Next, we characterize the geometry of such ascreen lightlike hypersurfaces.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.311-317
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• 2014

We study lightlike hypersurfaces of a semi-Riemannian space form $\tilde{M}(c)$ admitting a semi-symmetric non-metric connection. First, we construct a type of lightlike hypersurfaces according to the form of the structure vector field of $\tilde{M}(c)$, which is called a ascreen lightlike hypersurface. Next, we prove a characterization theorem for such an ascreen lightlike hypersurface endow with a totally geodesic screen distribution.