• Honam Mathematical Journal
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• v.36 no.2
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• pp.217-232
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• 2014

In this paper, we study the geometry of half lightlike submanifolds of an indefinite Kaehler manifold equipped with a quarter-symmetric metric connection. The main result is to prove several classification theorems for such half lightlike submanifolds.

• Honam Mathematical Journal
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• v.44 no.3
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• pp.432-446
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• 2022

This article introduces the structure of GCR-lightlike submanifolds of an indefinite Kaehler statistical manifold and derives their geometric properties. The characterizations on totally geodesic, mixed geodesic, D-geodesic and D'-geodesic GCR-lightlike submanifolds have also been obtained.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.847-863
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• 2023

We introduce the study of generic lightlike submanifolds of a semi-Riemannian product manifold. We establish a characterization theorem for the induced connection on a generic lightlike submanifold to be a metric connection. We also find some conditions for the integrability of the distributions associated with generic lightlike submanifolds and discuss the geometry of foliations. Then we search for some results enabling a generic lightlike submanifold of a semi-Riemannian product manifold to be a generic lightlike product manifold. Finally, we examine minimal generic lightlike submanifolds of a semi-Riemannian product manifold.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.1003-1022
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• 2017

The object of study in this paper is generic lightlike submanifolds of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection. We study the geometry of two types of generic light-like submanifolds, which are called recurrent and Lie recurrent generic lightlike submanifolds, of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.625-638
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• 2016

In this paper, we introduce the notion of semi-slant lightlike submanifolds of indefinite Sasakian manifolds giving characterization theorem with some non-trivial examples of such submanifolds. Integrability conditions of distributions $D_1$, $D_2$ and RadTM on semi-slant lightlike submanifolds of an indefinite Sasakian manifold have been obtained. We also obtain necessary and sufficient conditions for foliations determined by above distributions to be totally geodesic.

• 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.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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.515-531
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• 2018

Jin studied lightlike hypersurfaces of an indefinite Kaehler manifold [6, 8] or indefinite trans-Sasakian manifold [7] with a quarter-symmetric metric connection. Jin also studied generic lightlike submanifolds of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection [10]. We study generic lightlike submanifolds of an indefinite Kaehler manifold with a quarter-symmetric metric connection.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.215-221
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• 2010

In this paper, we study the geometry of half lightlike submanifolds of a Lorentzian manifold. The main result is a characterization theorem for irrotational screen homothetic half lightlike submanifolds of a Lorentzian space form.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.535-549
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• 2020

In this paper, we introduce the geometry of contact CR submanifolds and radical transversal lightlike submanifolds of Sasaki-like almost contact manifolds with B-metric. We obtain some new results that establish a relationship between these two submanifolds.