• 대한수학회논문집
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• 제32권1호
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• pp.119-133
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• 2017

In this paper, we study half lightlike submanifolds of an indefinite Kaehler manifold with a semi-symmetric non-metric connection. First, we characterize the geometry of two types of half lightlike submanifolds of such an indefinite Kaehler manifold. Next, we investigate the geometry of half lightlike submanifolds of an indefinite complex space form with a semi-symmetric non-metric connection.

• 대한수학회보
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• 제51권4호
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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.

• 대한수학회지
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• 제54권1호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권1호
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• pp.51-61
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• 2011

In this paper, we study the geometry of transversal half lightlike sub-manifolds of an indefinite Sasakian manifold. The main result is to prove three characterization theorems for such a transversal half lightlike submanifold. In addition to these main theorems, we study the geometry of totally umbilical transversal half lightlike submanifolds of an indefinite Sasakian manifold.

• 대한수학회보
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• 제54권2호
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• pp.429-442
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• 2017

In the present paper, screen isotropic leaves on lightlike hypersurfaces of a Lorentzian manifold are introduced and studied which are inspired by the definition of isotropic immersions in the Riemannian context. Some examples of such leaves are mentioned. Furthermore, some relations involving curvature invariants are obtained.

• 호남수학학술지
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• 제36권4호
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• pp.707-722
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• 2014

In this paper, we study the forms of the curvatures of lightlike submanifolds M of an indefinite Kenmotsu manifold $\bar{M}$ subject to the conditions: M is locally symmetric or M is semi-symmetric.

• 대한수학회논문집
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• 제30권1호
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• pp.35-43
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• 2015

We study two types of 1-lightlike submanifolds, so-called lightlike hypersurface and half lightlike submanifold, of an indefinite trans-Sasakian manifold $\bar{M}$ admitting non-metric ${\theta}$-connection. We prove that there exist no such two types of 1-lightlike submanifolds of an indefinite trans-Sasakian manifold $\bar{M}$ admitting non-metric ${\theta}$-connections.

• 대한수학회논문집
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• 제29권4호
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• pp.539-547
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• 2014

In this paper, we study two types 1-lightlike submanifolds M, so called lightlike hypersurface and half lightlike submanifold, of an indefinite Kaehler manifold $\bar{M}$ admitting non-metric ${\pi}$-connection. We prove that there exist no such two types 1-lightlike submanifolds of an indefinite Kaehler manifold $\bar{M}$ admitting non-metric ${\pi}$-connections.

• 대한수학회논문집
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• 제36권4호
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• pp.783-800
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• 2021

We prove the non-existence of warped product GCR-lightlike submanifolds of the type K_⊥ × _λ K_T such that K_T is a holomorphic submanifold and K_⊥ is a totally real submanifold in an indefinite Kaehler manifold $\tilde{K}$. Further, the existence of GCR-lightlike warped product submanifolds of the type K_T × _λ K_⊥ is obtained by establishing a characterization theorem in terms of the shape operator and the warping function in an indefinite Kaehler manifold. Consequently, we find some necessary and sufficient conditions for an isometrically immersed GCR-lightlike submanifold in an indefinite Kaehler manifold to be a GCR-lightlike warped product, in terms of the canonical structures f and ω. Moreover, we also derive a geometric estimate for the second fundamental form of GCR-lightlike warped product submanifolds, in terms of the Hessian of the warping function λ.

• 대한수학회보
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• 제52권1호
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• pp.201-213
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• 2015

In this paper, we study lightlike hypersurfaces of an indefinite Kaehler manifold with a quarter-symmetric metric connection. We prove several classification theorems for such a lightlike hypersurface.