• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.619-632
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• 2017

We define a new connection on semi-Riemannian manifold, which is called a non-metric ${\phi}$-symmetric connection. Semi-symmetric non-metric connection and quarter-symmetric non-metric connection are two impotent examples of this connection. The purpose of this paper is to study the geometry of lightlike hypersurfaces of an indefinite Kaehler manifold with a non-metric ${\phi}$-symmetric connection.

• East Asian mathematical journal
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• v.31 no.1
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• pp.27-32
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• 2015

In this paper, we study lightlike hypersurfaces M of a Lorentz manifold $\bar{M}$ with a semi-symmetric non-metric connection subject to the conditions; (1) the screen distribution S(TM) is totally geodesic in M, and (2) the second fundamental form B of M is parallel.

• East Asian mathematical journal
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• v.30 no.1
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• pp.15-22
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• 2014

In this paper, we study lightlike hypersurfaces M of semi-Riemannian manifolds $\bar{M}$ of quasi-constant curvatures. Our main result is a characterization theorem for screen homothetic Einstein lightlike hypersurfaces of a Lorentzian manifold of quasi-constant curvature subject such that its curvature vector field ${\zeta}$ is tangent to M.

• 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.

• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.111-125
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• 2012

In this paper, we introduce the notion of a slant lightlike submanifold of an indefinite Sasakian manifold. We provide a non-trivial example and obtain necessary and sufficient conditions for the existence of a slant lightlike submanifold. Also, we prove some characterization theorems.

• Journal of the Korean Mathematical Society
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• v.51 no.2
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• pp.311-323
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• 2014

In this paper, we construct two types of non-tangential half lightlike submanifolds of a semi-Riemannian manifold admitting a semi-symmetric non-metric connection. Our main result is to prove several characterization theorems for each types of such half lightlike submanifolds equipped with totally geodesic screen distributions.

• 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.44 no.3
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• pp.339-359
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• 2022

In this paper, we investigate k-Ricci curvature and k-scalar curvature on lightlike hypersurfaces of a real space form ${\tilde{M}}$(c) of constant sectional curvature c, endowed with semi-symmetric non-metric connection. Using this curvatures, we establish some inequalities for screen homothetic lightlike hypersurface of a real space form ${\tilde{M}}$(c) of constant sectional curvature c, endowed with semi-symmetric non-metric connection. Using these inequalities, we obtain some characterizations for such hypersurfaces. Considering the equality case, we obtain some results.

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.223-238
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• 2020

We study a lightlike hypersurface M of an indefinite nearly trans-Sasakian manifold ${\bar{M}}$ with an (ℓ, m)-type connection such that the structure vector field ζ of ${\bar{M}}$ is tangent to M. In particular, we focus on such lightlike hypersurfaces M for which the structure tensor field F is either recurrent or Lie recurrent, or such that M itself is totally umbilical or screen totally umbilical.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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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.