• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1271-1280
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• 2023

The object of the present paper is to introduce a type of non-flat Riemannian manifold, called a weakly cyclic generalized B-symmetric manifold (W CGBS)_n. We obtain a sufficient condition for a weakly cyclic generalized B-symmetric manifold to be a generalized quasi Einstein manifold. Next we consider conformally flat weakly cyclic generalized B-symmetric manifolds. Then we study Einstein (W CGBS)_n (n > 2). Finally, it is shown that the semi-symmetry and Weyl semi-symmetry are equivalent in such a manifold.

• 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.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1075-1089
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• 2018

We define a new connection on semi-Riemannian manifolds, which is a non-symmetric and non-metric connection. We say that this connection is an (${\ell}$, m)-type connection. Semi-symmetric non-metric connection and non-metric ${\phi}$-symmetric connection are two important 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 trans-Sasakian manifold with an (${\ell}$, m)-type connection.

• 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.

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.197-210
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• 2020

In this paper, we prove that there are no non-trivial 𝒫ℛ-semi-slant warped product submanifolds with proper slant coefficients in para-Kähler manifolds ${\bar{M}}$. We also present a numerical example that illustrates the existence of a 𝒫ℛ-warped product submanifold in ${\bar{M}}$.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.317-336
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• 2000

In this paper, when N is a compact Riemannian manifold, we discuss the method of using warped products to construct timelike or null future (or past) complete Lorentzian metrics on $M=(-{\infty},{\;}\infty){\;}{\times}f^N$ with specific scalar curvatures.

• 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).

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.207-216
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• 2014

The manifold $^*g-ESX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $^*g^{{\lambda}{\nu}}$ through the ES-connection which is both Einstein and semi-symmetric. The purpose of the present paper is to study the algebraic geometric structures of 3-dimensional $^*g-ESX_3$. Particularly, in 3-dimensional $^*g-ESX_3$, we derive a new set of powerful recurrence relations in the first class.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.319-330
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• 2016

The manifold $^*g-ESX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unied eld tensor $^*g^{{\lambda}{\nu}}$ through the ES-connection which is both Einstein and semi-symmetric. The purpose of the present paper is to study the algebraic geometric structures of 5-dimensional $^*g-ESX_5$. Particularly, in 5-dimensional $^*g-ESX_5$, we derive a new set of powerful recurrence relations in the first class.

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.127-135
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• 2017

The manifold $^*g-ESX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $^*g^{{\lambda}{\nu}}$ through the ES-connection which is both Einstein and semi-symmetric. The purpose of the present paper is to prove a necessary and sufficient condition for a unique Einstein's connection to exist in 5-dimensional $^*g-ESX_5$ and to display a surveyable tnesorial representation of 5-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations in the first class.