• The Pure and Applied Mathematics
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• v.20 no.2
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• pp.89-101
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• 2013

In this paper, we study half lightlike submanifolds M of an indefinite cosymplectic manifold $\bar{M}$, whose structure vector field is not tangent to M. First, we construct two types of such half lightlike submanifolds, named by transversal and normal half lightlike submanifolds. Next, we characterize the lightlike geometries of such two types half lightlike submanifolds.

• East Asian mathematical journal
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• v.24 no.4
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• pp.421-429
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• 2008

We study invariant lightlike submanifolds and almost contact CR-lightlike submanifolds of an indefinite cosymplectic manifold.

• The Pure and Applied Mathematics
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• v.21 no.1
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• pp.1-10
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• 2014

In this paper, we study the curvature of locally symmetric or semi-symmetric half lightlike submanifolds M of an indefinite Kenmotsu manifold $\bar{M}$, whose structure vector field is tangent to M. After that, we study the existence of the totally geodesic screen distribution of half lightlike submanifolds of indefinite Kenmotsu manifolds with parallel co-screen distribution subject to the conditions: (1) M is locally symmetric, or (2) the lightlike transversal connection is flat.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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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.

• East Asian mathematical journal
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• v.31 no.1
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• pp.33-40
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• 2015

We study the geometry of r-lightlike submanifolds M of a semi-Riemannian manifold $\bar{M}$ with a semi-symmetric non-metric connection subject to the conditions; (a) the screen distribution of M is totally geodesic in M, and (b) at least one among the r-th lightlike second fundamental forms is parallel with respect to the induced connection of M. The main result is a classification theorem for irrotational r-lightlike submanifold of a semi-Riemannian manifold of index r admitting a semi-symmetric non-metric connection.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.152-166
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• 2021

In this paper, we study the geometry of semi-slant lightlike submanifolds of an indefinite Kenmotsu manifold. The integrability conditions of distributions D1 ⊕ {V}, D2 ⊕ {V} and RadTM on semi-slant lightlike submanifolds of an indefinite Kenmotsu manifold are defined. Furthermore, we derive necessary and sufficient conditions for the above distributions to have totally geodesic foliations.

• 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 ${\bar{M}}$.

• East Asian mathematical journal
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• v.33 no.5
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• pp.533-542
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• 2017

We study the geometry of indefinite trans-Sasakian manifold ${\bar{M}}$ admitting a half lightlike submanifold M such that the structure vector field of ${\bar{M}}$ belongs to the transversal vector bundle of M. We prove several classification theorems of such an indefinite trans-Sasakian manifold.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.657-666
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• 2013

We study indefinite trans-Sasakian manifold $\bar{M}$ admitting an ascreen lightlike hypersurface M. Our main results are several classification theorems of such an indefinite trans-Sasakian manifold.

• The Pure and Applied Mathematics
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• v.18 no.2
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• pp.173-183
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• 2011

We study half lightlike submanifolds of an indefinite Sasakian manifold. The aim of this paper is to prove the following result: If a locally symmetric half lightlike submanifold of an indefinite Sasakian manifold is totally umbilical, then it is of constant positive curvature 1. In addition to this result, we prove three characterization theorems for such a half lightlike submanifold.