• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.327-339
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• 2012

In this paper we study $h$-projectively semisymmetric, ${\phi}$-pro-jectively semisymmetric, $h$-Weyl semisymmetric and ${\phi}$-Weyl semisym- metric non-Sasakian ($k$, ${\mu}$)-contact metric manifolds. In all the cases the manifold becomes an ${\eta}$-Einstein manifold. As a consequence of these results we obtain that if a 3-dimensional non-Sasakian ($k$, ${\mu}$)-contact metric manifold satisfies such curvature conditions, then the manifold reduces to an N($k$)-contact metric manifold.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.297-306
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• 2012

In this paper we study (${\epsilon}$)-Lorentzian para-Sasakian manifolds and show its existence by an example. Some basic results regarding such manifolds have been deduced. Finally, we study conformally flat and Weyl-semisymmetric (${\epsilon}$)-Lorentzian para-Sasakian manifolds.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.435-445
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• 2005

The purpose of this paper is to study a Kenmotsu manifold which is derived from the almost contact Riemannian manifold with some special conditions. In general, we have some relations about semi-symmetric, Ricci semi-symmetric or Weyl semisymmetric conditions in Riemannian manifolds. In this paper, we partially classify the Kenmotsu manifold and consider the manifold admitting a transformation which keeps Riemannian curvature tensor and Ricci tensor invariant.

• Communications of the Korean Mathematical Society
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• v.26 no.4
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• pp.623-634
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• 2011

The object of the present paper is to study N(${\kappa}$)-quasi Einstein manifolds. Existence of N(${\kappa}$)-quasi Einstein manifolds are proved. Physical example of N(${\kappa}$)-quasi Einstein manifold is also given. Finally, Weyl-semisymmetric N(${\kappa}$)-quasi Einstein manifolds have been considered.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1233-1247
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• 2023

The aim of the present paper is to study complete lifts of a semi-symmetric non-metric connection from a Riemannian manifold to its tangent bundles. Some curvature properties of a Riemannian manifold to its tangent bundles with respect to such a connection have been investigated.