• 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.17 no.1
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• pp.51-63
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• 2010

In this paper, we prove two characterization theorems for real half lightlike submanifold (M,g,S(TM)) of an indefinite Kaehler manifold $\bar{M}$ or an indefinite complex space form $\bar{M}$(c) subject to the conditions : (a) M is totally umbilical in $\bar{M}$, or (b) its screen distribution S(TM) is totally umbilical in M.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.443-450
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• 2010

In this paper, we study the geometry of lightlike real hyper-surfaces of an indefinite Kaehler manifold. The main result is a characterization theorem for lightlike real hypersurfaces M of an indefinite complex space form $\bar{M}(c)$ such that the screen distribution is totally umbilic.

• 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.27 no.4
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• pp.763-770
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• 2012

In this paper, we study the geometry lightlike hypersurfaces (M, $g$, S(TM)) of a semi-Riemannian manifold ($\tilde{M}$, $\tilde{g}$) of quasi-constant curvature subject to the conditions: (1) The curvature vector field of $\tilde{M}$ is tangent to M, and (2) the screen distribution S(TM) is either totally geodesic in M or totally umbilical in $\tilde{M}$.

• 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.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.365-377
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• 2016

In this paper, we study half lightlike submanifolds M of an indefinite Kaehler manifold $\bar{M}$ of quasi-constant curvature such that the characteristic vector field ${\zeta}$ of $\bar{M}$ is tangent to M. First, we provide a new result for such a half lightlike submanifold. Next, we investigate a statical half lightlike submanifold M of $\bar{M}$ subject such that (1) the screen distribution S(TM) is totally umbilical or (2) M is screen conformal.

• East Asian mathematical journal
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• v.32 no.1
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• pp.1-11
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• 2016

We study transversal half lightlike submanifolds of an indefinite Kaehler manifold of a quasi-constant curvature. First, we provide a new result for such a transversal half lightlike submanifold. Next, we investigate a statical half lightlike submanifold M such that (1) the screen distribution S(TM) is totally umbilical, or (2) M is screen homothetic.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.361-375
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• 2021

The object of the present paper is to deduce some important results on generic submanifolds and also generic product of LP-Sasakian manifolds with concurrent vector fields. Also, we provide a necessary and sufficient condition for which the invariant distribution D and anti-invariant distribution D^⊥ of M are Einstein. Also, we deduce an interesting necessary and sufficient condition for submanifolds of LP-Sasakian manifolds to be totally umbilical submanifolds. Especially we deal with the generic submanifolds admitting a Ricci soliton in LP-Sasakian manifolds endowed with concurrent vector fields.