• 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.

• 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.

• East Asian mathematical journal
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• v.26 no.1
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• pp.75-79
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• 2010

Let G be a compact connected semisimple Lie group, g the Lie algebra of G, g the canonical metric (the biinvariant Riemannian metric which is induced from the Killing form of g), and $\nabla$ be the Levi-Civita connection for the metric g. Then, we get the fact that the Levi-Civita connection $\nabla$ in the tangent bundle TG over (G, g) is a Yang-Mills connection.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.73-90
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• 2012

We define a quarter-symmetric non-metric connection in a nearly trans-Sasakian manifold and we consider semi-invariant submanifolds of a nearly trans-Sasakian manifold endowed with a quarter-symmetric non-metric connection. Moreover, we also obtain integrability conditions of the distributions on semi-invariant submanifolds.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.25-32
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• 2012

We define a quarter symmetric metric connection in a Lorentzia para-Sasakian manifold and study CR-submanifolds of a Lorentzian para-Sasakian manifold endowed with a quarter symmetric metric connection. Moreover, we also obtain integrability conditions of the distributions on CR-submanifolds.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.1113-1129
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• 2019

We define a class of semi-symmetric metric connection on a Riemannian manifold for which the conformal, the projective, the concircular, the quasi conformal and the m-projective curvature tensors are invariant. We also study the properties of semisymmetric, Ricci semisymmetric and Eisenhart problems for solving second order parallel symmetric and skew-symmetric tensors on the Riemannian manifolds equipped with a semi-symmetric metric P-connection.

• 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.

• Honam Mathematical Journal
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• v.45 no.4
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• pp.655-667
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• 2023

In this paper, we study quasi-Sasakian 3-dimensional manifolds admitting generalized 𝜂-Ricci solitons associated to the Schouten-van Kampen connection. We give an example of generalized 𝜂-Ricci solitons on a quasi-Sasakian 3-dimensional manifold with respect to the Schouten-van Kampen connection to prove our results.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.803-817
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• 2020

The object of the present paper is to study 𝜂-Ricci soliton on Kenmotsu manifold with respect to general connection.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1203-1219
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• 2020

Jin [7] defined a new connection on semi-Riemannian manifolds, which is a non-symmetric and non-metric connection. He said that this connection is an (ℓ, m)-type connection. Jin also studied lightlike hypersurfaces of an indefinite trans-Sasakian manifold with an (ℓ, m)-type connection in [7]. We study further the geometry of this subject. In this paper, we study generic lightlike submanifolds of an indefinite trans-Sasakian manifold endowed with an (ℓ, m)-type connection.