• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.105-116
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• 2018

In this paper, the object is to study a semi-symmetric non-metric connection on an LP-Sasakian manifold whose concircular curvature tensor satisfies certain curvature conditions.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1171-1184
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• 2016

We define a new connection on semi-Riemannian manifolds, which is called a symmetric connection of type (${\ell}$, m). Semi-symmetric connection and quarter-symmetric connection are two examples of this connection such that $({\ell},m)=(1,0)$ and $({\ell},m)=(0,1)$ respectively. In this paper, we study lightlike hypersurfaces of an indefinite Kaehler manifold endowed with a symmetric metric connection of type (${\ell}$, m).

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.1033-1045
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• 2017

The conharmonic curvature tensor under certain conditions has been studied for Kenmotsu manifolds with respect to the semi-symmetric metric connection.

• Honam Mathematical Journal
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• v.42 no.3
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• pp.621-643
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• 2020

Depending on the characteristic vector filed ζ, a generic lightlike submanifold M in an indefinite Kaehler manifold ${\bar{M}}$ with a semi-symmetric metric connection has various characterizations. In this paper, when the characteristic vector filed ζ belongs to the screen distribution S(TM) of M, we provide some characterizations of (Lie-) recurrent generic lightlike submanifold M in an indefinite Kaehler manifold ${\bar{M}}$ with a semi-symmetric metric connection. Moreover, we characterize various generic lightlike submanifolds in an indefinite complex space form ${\bar{M}}$ (c) with a semi-symmetric metric connection.

• Korean Journal of Mathematics
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• v.32 no.3
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• pp.407-424
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• 2024

The present work aims to introduce the geometry of invariant and screen semi-invariant lightlike submanifolds of a metallic semi-Riemannian manifold equipped with a quarter symmetric non-metric connection. The study establishes the characterization of integrability and parallelism of the distributions inherent in these submanifolds. Additionally, the conditions for distributions defining totally geodesic foliations on the invariant and screen semi-invariant lightlike submanifolds of metallic semi-Riemannian manifold are specified.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.825-837
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• 2022

We characterize a three-dimensional Riemannian manifold endowed with a type of semi-symmetric metric P-connection. At first, it is proven that if the metric of such a manifold is a gradient m-quasi-Einstein metric, then either the gradient of the potential function 𝜓 is collinear with the vector field P or, λ = -(m + 2) and the manifold is of constant sectional curvature -1, provided P𝜓 ≠ m. Next, it is shown that if the metric of the manifold under consideration is a gradient 𝜌-Einstein soliton, then the gradient of the potential function is collinear with the vector field P. Also, we prove that if the metric of a 3-dimensional manifold with semi-symmetric metric P-connection is a gradient 𝜔-Ricci soliton, then the manifold is of constant sectional curvature -1 and λ + 𝜇 = -2. Finally, we consider an example to verify our results.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.613-624
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• 2016

We define a new connection on a semi-Riemannian manifold. Its notion contains two well known notions; (1) semi-symmetric connection and (2) quarter-symmetric connection. In this paper, we study the geometry of lightlike hypersurfaces of an indefinite generalized Sasakian space form with a symmetric metric connection of type (${\ell}$, m).

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.537-562
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• 2019

The aim of the present paper is to study the ${\delta}$-Lorentzian trans-Sasakian manifold endowed with semi-symmetric metric connections admitting ${\eta}$-Ricci Solitons and Ricci Solitons. We find expressions for the curvature tensor, the Ricci curvature tensor and the scalar curvature tensor of ${\delta}$-Lorentzian trans-Sasakian manifolds with a semisymmetric-metric connection. Also, we discuses some results on quasi-projectively flat and ${\phi}$-projectively flat manifolds endowed with a semi-symmetric-metric connection. It is shown that the manifold satisfying ${\bar{R}}.{\bar{S}}=0$, ${\bar{P}}.{\bar{S}}=0$ is an ${\eta}$-Einstein manifold. Moreover, we obtain the conditions for the ${\delta}$-Lorentzian trans-Sasakian manifolds with a semisymmetric-metric connection to be conformally flat and ${\xi}$-conformally flat.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.895-903
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• 2009

We define a semi-symmetric metric connection in an almost $\gamma$-paracontact Riemannian manifold and we consider invariant, non-invariant and anti-invariant hypersurfaces of an almost $\gamma$-paracontact Riemannian manifold endowed with a semi-symmetric metric 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.