• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.1089-1103
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• 2010

In this paper, we study lightlike submanifolds of a semi-Riemannian manifold admitting a semi-symmetric non-metric connection. We obtain a necessary and a sufficient condition for integrability of the screen distribution. Then we give the conditions under which the Ricci tensor of a lightlike submanifold with a semi-symmetric non-metric connection is symmetric. Finally, we show that the Ricci tensor of a lightlike submanifold of semi-Riemannian space form is not parallel with respect to the semi-symmetric non-metric connection.

• Communications of the Korean Mathematical Society
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• v.28 no.1
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• pp.163-175
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• 2013

In this paper, we prove a classification theorem for Einstein lightlike hypersurfaces M of a Lorentzian space form ($\bar{M}$(c), $\bar{g}$) with a semi-symmetric metric connection subject such that the second fundamental forms of M and its screen distribution S(TM) are conformally related by some non-zero constant.

• 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.1
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• pp.185-195
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• 2020

This paper aims to study the 𝒲^⁎-curvature tensor on relativistic space-times. The energy-momentum tensor T of a space-time having a semi-symmetric 𝒲^⋆-curvature tensor is semi-symmetric, whereas the whereas the energy-momentum tensor T of a space-time having a divergence free 𝒲^⋆-curvature tensor is of Codazzi type. A space-time having a traceless 𝒲^⁎-curvature tensor is Einstein. A 𝒲^⁎-curvature flat space-time is Einstein. Perfect fluid space-times which admits 𝒲^⋆-curvature tensor are considered.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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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.

• East Asian mathematical journal
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• v.30 no.3
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• pp.371-383
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• 2014

We study the geometry of lightlike submanifolds of a semi-Riemannian manifold. The purpose of this paper is to prove two singular theorems for irrotational lightlike submanifolds M of a semi-Riemannian space form $\bar{M}(c)$ admitting a semi-symmetric non-metric connection such that the structure vector field of $\bar{M}(c)$ is tangent to M.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.809-818
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• 2013

We study irrotational half lightlike submanifolds M of a semi-Riemannian space form with a semi-symmetric non-metric connection such that its structure vector field is tangent to M. We prove two characterization theorems for such an irrotational half lightlike submanifold.

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.367-376
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• 2006

We investigate semi-symmetry and pseudo-symmetry of some 3-dimensional Riemannian manifolds: the D'Atri spaces, the Thurston geometries as well as the ${\eta}$-Einstein manifolds. We prove that all these manifolds are pseudo-symmetric and that many of them are not semi-symmetric.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.213-219
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• 2014

We prove that a semi-symmetric 3-dimensional gradient Ricci soliton is locally isometric to a space form $\mathbb{S}^3$, $\mathbb{H}^3$, $\mathbb{R}^3$ (Gaussian soliton); or a product space $\mathbb{R}{\times}\mathbb{S}^2$, $\mathbb{R}{\times}\mathbb{H}^2$, where the potential function depends only on the nullity.