• 호남수학학술지
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• 제40권2호
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• pp.325-346
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• 2018

The object of the present paper is to study some types of Ricci pseudosymmetric $(LCS)_n$-manifolds whose metric is Ricci soliton. We found the conditions when Ricci soliton on concircular Ricci pseudosymmetric, projective Ricci pseudosymmetric, $W_3$-Ricci pseudosymmetric, conharmonic Ricci pseudosymmetric, conformal Ricci pseudosymmetric $(LCS)_n$-manifolds to be shrinking, steady and expanding. We also construct an example of concircular Ricci pseudosymmetric $(LCS)_3$-manifold whose metric is Ricci soliton.

• 대한수학회논문집
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• 제33권1호
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• pp.261-272
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• 2018

The object of the present paper is to study some curvature properties of almost Kenmotsu manifolds with conformal Reeb foliation. Among others it is proved that an almost Kenmotsu manifold with conformal Reeb foliation is Ricci semisymmetric if and only if it is an Einstein manifold. Finally, we study Yamabe soliton in this manifold.

• Kyungpook Mathematical Journal
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• 제48권2호
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• pp.183-194
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• 2008

We prove that totally umbilical submanifold M of an extended quasi-recurren manifold is also extended quasi-recurrent. If, moreover, M is conformally flat then, locally, M is isometric to the manifold with known metric. Some curvature properties of such submanifold are investigated. Making use of these results we shall prove the existence of totally umbilical submanifold being pseudosymmetric in the sense of Ryszard Deszcz and satisfying some other curvature conditions.

• 대한수학회논문집
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• 제24권3호
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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.

• 대한수학회논문집
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• 제25권4호
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• pp.615-621
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• 2010

We study pseudo symmetric (briefly $(PS)_n$) and pseudo Ricci symmetric (briefly $(PRS)_n$) warped product manifolds $M{\times}_FN$. If M is $(PS)_n$, then we give a condition on the warping function that M is a pseudosymmetric space and N is a space of constant curvature. If M is $(PRS)_n$, then we show that (i) N is Ricci symmetric and (ii) M is $(PRS)_n$ if and only if the tensor T defined by (2.6) satisfies a certain condition.

• Korean Journal of Mathematics
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• 제29권4호
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• pp.801-810
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• 2021

This paper deals with the study of N (k)-quasi Einstein manifolds that satisfies the certain curvature conditions 𝒞_*·𝒞_* = 0, 𝓢·𝒞_* = 0 and ${\mathcal{R}}{\cdot}{\mathcal{C}}_*=f{\tilde{Q}}(g,\;{\mathcal{C}}_*)$, where 𝒞_*, 𝓢 and 𝓡 denotes the quasi-conformal curvature tensor, Ricci tensor and the curvature tensor respectively. Finally, we construct an example of N (k)-quasi Einstein manifold.

• 호남수학학술지
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• 제45권2호
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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.