• The Pure and Applied Mathematics
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• v.17 no.1
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• pp.29-38
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• 2010

We study the geometry of half light like submanifold M of a semi-Riemannian space form $\bar{M}$(c) subject to the conditions : (a) the screen distribution on M is totally umbilic in M and the coscreen distribution on M is conformal Killing on $\bar{M}$ or (b) the screen distribution is totally geodesic in M and M is irrotational.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.725-743
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• 2017

We prove that there exist foliations whose leaves are the maximal integral null manifolds immersed as submanifolds of indefinite locally conformal cosymplectic manifolds. Necessary and sufficient conditions for such leaves to be screen conformal, as well as possessing integrable distributions are given. Using Newton transformations, we show that any compact ascreen null leaf with a symmetric Ricci tensor admits a totally geodesic screen distribution. Supporting examples are also obtained.

• The Pure and Applied Mathematics
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• v.21 no.1
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• pp.39-50
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• 2014

In this paper, we study screen quasi-conformal irrotational half lightlike submanifolds M of a semi-Riemannian space form $\tilde{M}(c)$ admitting a semi-symmetric non-metric connection, whose structure vector field ${\zeta}$ is tangent to M. The main result is a classification theorem for such Einstein half lightlike submanifolds of a Lorentzian space form admitting a semi-symmetric non-metric connection.

• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.211-228
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• 2012

We study lightlike submanifolds M of a semi-Riemannian manifold $\bar{M}$ with a semi-symmetric non-metric connection subject to the conditions; (a) the characteristic vector field of $\bar{M}$ is tangent to M, (b) the screen distribution on M is totally umbilical in M and (c) the co-screen distribution on M is conformal Killing.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.769-781
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• 2011

We study the geometry of half lightlike sbmanifolds M of a semi-Riemannian space form $\tilde{M}(c)$ admitting a semi-symmetric metric connection subject to the conditions: (1) The screen distribution S(TM) is totally umbilical (geodesic) and (2) the co-screen distribution $S(TM^{\bot})$ of M is a conformal Killing one.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.487-504
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• 2008

In this paper we study the geometry of codimension 2 screen conformal Einstein half lightiike submanifolds M of a semi-Riemannian manifold $(\={M}(c),\={g})$ of constant curvature c, with a Killing co-screen distribution on $\={M}$. The main result is a classification theorem for screen homothetic Einstein half lightlike submanifold of Lorentzian space forms.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.195-213
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• 2020

We define two types of null hypersurfaces as; isoparametric and quasi isoparametric null hypersurfaces of Lorentzian space forms, based on the two shape operators associated with a null hypersurface. We prove that; on any screen conformal isoparametric null hypersurface, the screen geodesics lie on circles in the ambient space. Furthermore, we prove that the screen distributions of isoparametric (or quasi isoparametric) null hypersurfaces with at most two principal curvatures are generally Riemannian products. Several examples are also given to illustrate the main concepts.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.979-994
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• 2014

We study half lightlike submanifold M of an indefinite trans-Sasakian manifold such that its structure vector field is tangent to M. First we study the general theory for such half lightlike submanifolds. Next we prove some characterization theorems for half lightlike submanifolds of an indefinite generalized Sasakian space form.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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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 $T\bar{M}$.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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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.