• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.795-808
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• 2012

The object of the present paper is to study 3-dimensional trans-Sasakian manifolds with conservative curvature tensor and also 3-dimensional conformally flat trans-Sasakian manifolds. Next we consider compact connected $\eta$-Einstein 3-dimensional trans-Sasakian manifolds. Finally, an example of a 3-dimensional trans-Sasakian manifold is given, which verifies our results.

• Honam Mathematical Journal
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• v.41 no.3
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• pp.489-503
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• 2019

The aim of this paper is to study three-dimensional conformally flat quasi-para-Sasakian manifolds. First, the necessary and sufficient conditions are provided for three-dimensional quasipara-Sasakian manifolds to be conformally flat. Next, a characterization of three-dimensional conformally flat quasi-para-Sasakian manifold is given. Finally, a method for constructing examples of three-dimensional conformally flat quasi-para-Sasakian manifolds is presented.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.485-495
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• 2022

The aim of this paper is to characterize K-contact and Sasakian manifolds whose metrics are generalized quasi-Einstein metric. It is proven that if the metric of a K-contact manifold is generalized quasi-Einstein metric, then the manifold is of constant scalar curvature and in the case of a Sasakian manifold the metric becomes Einstein under certain restriction on the potential function. Several corollaries have been provided. Finally, we consider Sasakian 3-manifold whose metric is generalized quasi-Einstein metric.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.577-589
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• 2023

The aim of the present paper is to study LP-Sasakian manifolds admitting *-Einstein soliton satisfying certain curvature conditions. Finally, we have constructed a 3-dimensional example of an LP-Sasakian manifold admitting *-Einstein soliton.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.645-660
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• 2021

This paper examines the behavior of a 3-dimensional trans-Sasakian manifold equipped with a gradient generalized quasi-Yamabe soliton. In particular, It is shown that α-Sasakian, β-Kenmotsu and cosymplectic manifolds satisfy the gradient generalized quasi-Yamabe soliton equation. Furthermore, in the particular case when the potential vector field ζ of the quasi-Yamabe soliton is of gradient type ζ = grad(ψ), we derive a Poisson's equation from the quasi-Yamabe soliton equation. Also, we study harmonic aspects of quasi-Yamabe solitons on 3-dimensional trans-Sasakian manifolds sharing a harmonic potential function ψ. Finally, we observe that 3-dimensional compact trans-Sasakian manifold admits the gradient generalized almost quasi-Yamabe soliton with Hodge-de Rham potential ψ. This research ends with few examples of quasi-Yamabe solitons on 3-dimensional trans-Sasakian manifolds.

• Honam Mathematical Journal
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• v.42 no.3
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• pp.601-620
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• 2020

In this paper, firstly we discuss some basic axioms of trans Sasakian manifolds. Later, the trans-Sasakian manifold with quarter symmetric non-metric connection are studied and its curvature tensor and Ricci tensor are calculated. Also, we study the η-Ricci solitons on a Trans-Sasakian Manifolds with quartersymmetric non-metric connection. Indeed, we investigated that the Ricci and η-Ricci solitons with quarter-symmetric non-metric connection satisfying the conditions ${\tilde{R}}.{\tilde{S}}$ = 0. In a particular case, when the potential vector field ξ of the η-Ricci soliton is of gradient type ξ = grad(ψ), we derive, from the η-Ricci soliton equation, a Laplacian equation satisfied by ψ. Finally, we furnish an example for trans-Sasakian manifolds with quarter-symmetric non-metric connection admitting the η-Ricci solitons.

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.793-801
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• 2019

The aim of the present paper is to study certain recurrent properties of LP-Sasakian manifolds. Here we first describe Ricci ${\eta}$-recurrent LP-Sasakian manifolds. Further we study semi-generalized recurrent and three dimensional locally generalized concircularly ${\phi}$-recurrent LP-Sasakian manifolds and got interesting results.

• Honam Mathematical Journal
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• v.45 no.3
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• pp.471-490
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• 2023

In this present paper, we study QSM-connection (quarter-symmetric metric connection) on Sasakian statistical manifolds. Firstly, we express the relation between the QSM-connection ${\tilde{\nabla}}$ and the torsion-free connection ∇ and obtain the relation between the curvature tensors ${\tilde{R}}$ of ${\tilde{\nabla}}$ and R of ∇. After then we obtain these relations for ${\tilde{\nabla}}$ and the dual connection ∇^* of ∇. Also, we give the relations between the curvature tensor ${\tilde{R}}$ of QSM-connection ${\tilde{\nabla}}$ and the curvature tensors R and R^* of the connections ∇ and ∇^* on Sasakian statistical manifolds. We obtain the relations between the Ricci tensor of QSM-connection ${\tilde{\nabla}}$ and the Ricci tensors of the connections ∇ and ∇^*. After these, we construct an example of a 3-dimensional Sasakian manifold admitting the QSM-connection in order to verify our results. Finally, we study the submanifolds with the induced connection with respect to QSM-connection of statistical manifolds.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.377-387
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• 2021

In the present paper, we characterize quasi-Sasakian 3-manifolds admitting 𝜂-Ricci solitons. Finally, the existence of 𝜂-Ricci soliton in a quasi-Sasakian 3-manifold has been proved by a concrete example.

• Honam Mathematical Journal
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• v.45 no.4
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• pp.655-667
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• 2023

In this paper, we study quasi-Sasakian 3-dimensional manifolds admitting generalized 𝜂-Ricci solitons associated to the Schouten-van Kampen connection. We give an example of generalized 𝜂-Ricci solitons on a quasi-Sasakian 3-dimensional manifold with respect to the Schouten-van Kampen connection to prove our results.