• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.179-191
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• 2022

We set our target to investigate Yamabe solitons, gradient Yamabe solitons and gradient Einstein solitons within the structure of 3-dimensional non-cosymplectic normal almost contact metric manifolds. Also, we provide a nontrivial example and validate a result of our paper.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.115-122
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• 2021

In this current article, we intend to investigate k-almost Yamabe and gradient k-almost Yamabe solitons inside the setting of three-dimensional Kenmotsu manifolds.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.851-863
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• 2018

We derive lower bounds of the scalar curvature on complete non-compact gradient Yamabe solitons under some integral curvature conditions. Based on this, we prove that potential functions of Yamabe solitons have at most quadratic growth for distance function. We also obtain a finite topological type property on complete shrinking gradient Yamabe solitons under suitable scalar curvature assumptions.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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• pp.219-226
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• 2020

In this paper, we consider gradient Ricci solitons and gradient Yamabe solitons in the warped product spaces. Also we study warped product space with harmonic curvature related to gradient Ricci solitons and gradient Yamabe solitons. Consequently some theorems are generalized and we derive differential equations for a warped product space to be a gradient Ricci soliton.

• Kyungpook Mathematical Journal
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• v.63 no.4
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• pp.639-645
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• 2023

An almost Yamabe soliton is a generalization of the Yamabe soliton. In this article, we deduce some results regarding almost gradient Yamabe solitons. More specifically, we show that a compact almost gradient Yamabe soliton having non-negative Ricci curvature is trivial. Again, we prove that an almost gradient Yamabe soliton with a non-negative potential function and scalar curvature bound admitting an integral condition is trivial. Moreover, we give a characterization of a compact almost gradient Yamabe solitons.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.261-268
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• 2020

In this paper, we study gradient Yamabe solitons in the warped product manifolds and classify the warped product manifolds with gradient Yamabe solitons. Moreover we investigate the admitness of gradient Yamabe solitons and geometric structures for some model spaces.

• Honam Mathematical Journal
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• v.42 no.3
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• pp.521-536
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• 2020

The object of the present paper is to study of Almost Quasi-Yamabe solitons and gradient almost quasi-Yamabe solitons on an Lorentzian concircular structure manifolds briefly say (LCS)_n-manifolds under infinitesimal CL-transformations and obtained sufficient conditions for such solitons to be expanding, steady and shrinking. Also we obtained a necessary and sufficient condition of an almost quasi-Yamabe soliton with respect to the CL-connection to be an almost quasi-Yamabe soliton on (LCS)_n-manifolds with respect to Levi-Civita connection. Finally, we construct an example of steady almost quasi-Yamabe soliton on 3-dimensional (LCS)_n-manifolds.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.813-822
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• 2021

The aim of this paper is to characterize a Kenmotsu 3-manifold whose metric is either a Ricci-Yamabe soliton or gradient Ricci-Yamabe soliton. Finally, we verify the obtained results by an example.

• 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.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.321-331
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• 2019

The present paper deals with a study of infinitesimal CL-transformations on Kenmotsu manifolds, whose metric is Yamabe soliton and obtained sufficient conditions for such solitons to be expanding, steady and shrinking. Among others, we find a necessary and sufficient condition of a Yamabe soliton on Kenmotsu manifold with respect to CL-connection to be Yamabe soliton on Kenmotsu manifold with respect to Levi-Civita connection. We found the necessary and sufficient condition for the Yamabe soliton structure to be invariant under Schouten-Van Kampen connection. Finally, we constructed an example of steady Yamabe soliton on 3-dimensional Kenmotsu manifolds with respect to Schouten-Van Kampen connection.