• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권2호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권1호
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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.

• 대한수학회논문집
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• 제29권1호
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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.

• 대한수학회보
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• 제60권4호
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• pp.1003-1016
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• 2023

In this paper, we introduce the idea of twisted product lightlike submanifolds of semi-Riemannian manifolds and provide non-trivial examples of such lightlike submanifolds. Then, we prove the non-existence of proper isotropic or totally lightlike twisted product submanifolds of a semi-Riemannian manifold. We also show that for a twisted product lightlike submanifold of a semi-Riemannian manifold, the induced connection ∇ is not a metric connection. Further, we prove that a totally umbilical SCR-lightlike submanifold of an indefinite Kaehler manifold ${\tilde{M}}$ does not admit any twisted product SCR-lightlike submanifold of the type M_⊥×_ϕM_T, where M_⊥ is a totally real submanifold and MT is a holomorphic submanifold of ${\tilde{M}}$. Consequently, we obtain a geometric inequality for the second fundamental form of twisted product SCR-lightlike submanifolds of the type M_T×_ϕM_⊥ of an indefinite Kaehler manifold ${\tilde{M}}$, in terms of the gradient of ln ϕ, where ϕ stands for the twisting function. Subsequently, the equality case of this inequality is discussed. Finally, we construct a non-trivial example of a twisted product SCR-lightlike submanifold in an indefinite Kaehler manifold.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권3호
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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.

• 대한수학회논문집
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• 제35권3호
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• pp.979-998
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• 2020

We study totally umbilical real half lightlike submanifolds of indefinite Kaehler manifolds with a quarter-symmetric metric connection. We obtain some conditions for a real half lightlike submanifold of an indefinite Kaehler manifold with a quarter-symmetric metric connection to be a product manifold. We derive the expression for induced Ricci type tensor 𝓡^(0,2) and also obtain conditions for 𝓡^(0,2) to be symmetric.

• 대한수학회보
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• 제50권3호
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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.

• 충청수학회지
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• 제24권4호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권1호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권4호
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• pp.353-359
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• 2011

In this paper, we characterize a semi-Riemannian manifolds satisfies the axiom of indefinite surfaces. We obtain the following result: If a semi-Riemannian manifold satisfies the axiom of indefinite surfaces, then it is a real space form.