• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.415-424
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• 2009

The object of the present paper is to study the generalized quasi-Einstein manifolds satisfying some conditions. Finally the existence of such manifolds is ensured by several interesting examples.

• Korean Journal of Mathematics
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• v.10 no.2
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• pp.157-166
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• 2002

We show that the contact conformal curvature tensor on 3-dimensional Sasakian manifold always vanishes. We also prove that if the contact conformal curvature tensor vanishes on a 3-dimensional locally ${\varphi}$-symmetric contact metric manifold M, then M is a Sasakian space form.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.269-278
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• 2020

This paper aims to study the geometrical properties of the conharmonic curvature tensor of a locally conformal almost cosymplectic manifold. The necessary and sufficient conditions for the conharmonic curvature tensor to be flat, the locally conformal almost cosymplectic manifold to be normal and an η-Einstein manifold were determined.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.25-29
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• 1992

The purpose of this paper is to study indefinite Kaehlerian metrics with vanishing conformal curvature tensor field. In the first section, a brief summary of the complex version of indefinite Kaehlerian manifolds is recalled and we introduce the conformal curvature tensor field on an indefinite Kaehlerian manifold. In section 2, we obtain the theorem for indefinite Kaehlerian metrics with vanishing conformal curvature tensor field.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.789-799
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• 2009

In this study we consider ${\varphi}$-conformally flat, ${\varphi}$-conharmonically flat, ${\varphi}$-projectively at and ${\varphi}$-concircularly flat Lorentzian ${\alpha}$-Sasakian manifolds. In all cases, we get the manifold will be an ${\eta}$-Einstein manifold.

• Honam Mathematical Journal
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• v.45 no.2
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• pp.215-230
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• 2023

In this article, generalized Sasakian space forms are investigated on W₀ -curvature tensor. Characterizations of generalized Sasakian space forms are obtained on W₀-curvature tensor. Special curvature conditions established with the help of Riemann, Ricci, concircular, projective curvature tensors are discussed on W₀-curvature tensor. With the help of these curvature conditions, important characterizations of generalized Sasakian space forms are obtained. In addition, the concepts of W₀-pseudosymmetry and W₀ -Ricci pseudosymmetry are defined and the behavior according to these concepts for the generalized Sasakian space form is examined.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.313-319
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• 2008

The object of the paper is to study a Sasakian manifold with quasi-conformal curvature tensor.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.337-343
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• 1998

In this paper we show that every contact metric manifold with vanishing contact conformal curvature tensor is a Sasakian space form.

• East Asian mathematical journal
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• v.22 no.1
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• pp.111-130
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• 2006

We study cosymplectic submersions with vanishing cosymplectic Bochner curvature tensor.

• Korean Journal of Mathematics
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• v.21 no.1
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• pp.91-100
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• 2013

This paper is a direct continuation of [1] and [2]. In this paper we investigate some properties of ES-curvature tensor and contracted ES-curvature tensor of g - $ESX_n$. Also, we study the field equations in the n-dimensional ES manifold g - $ESX_n$.