• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.313-324
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• 2023

In the present paper, we study generalized Ricci solitons on N(κ)-contact metric manifolds, in particular, we consider when the potential vector field is the concircular vector field. We also consider generalized gradient Ricci solitons, and verify our results with an example.

• Kyungpook Mathematical Journal
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• v.64 no.2
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• pp.261-270
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• 2024

In this paper, we consider generalized 𝜂-Ricci solitons associated to the general connection on Kenmotsu manifolds. We confirm the existence of such solitons by constructing a non-trivial example, and we obtain some properties of Kenmotsu manifolds that admit the generalized 𝜂-Ricci solitons associated with the general connection.

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.715-728
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• 2022

The aim of this article is to study the h-almost Ricci solitons and h-almost gradient Ricci solitons on generalized Sasakian-space-forms. First, we consider h-almost Ricci soliton with the potential vector field V as a contact vector field on generalized Sasakian-space-form of dimension greater than three. Next, we study h-almost gradient Ricci solitons on a three-dimensional quasi-Sasakian generalized Sasakian-space-form. In both the cases, several interesting results are obtained.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.175-186
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• 2024

In this paper, we study para-Kenmotsu manifolds admitting generalized η-Ricci solitons associated to the Zamkovoy connection. We provide an example of generalized η-Ricci soliton on a para-Kenmotsu manifold to prove our results.

• 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.

• 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.

• Honam Mathematical Journal
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• v.40 no.2
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• pp.367-376
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• 2018

The object of the present paper is to study the Kenmotsu manifolds which metric tensor is ${\eta}$-Ricci soliton. We bring out curvature conditions for which Ricci solitons in Kenmotsu manifolds are sometimes shrinking or expanding and some other times steady.

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.341-358
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• 2023

Our aim is to study the properties of Fischer-Marsden conjecture and Ricci-Bourguignon solitons within the framework of generalized Sasakian-space-forms with 𝛽-Kenmotsu structure. It is proven that a (2n + 1)-dimensional generalized Sasakian-space-form with 𝛽-Kenmotsu structure satisfying the Fischer-Marsden equation is a conformal gradient soliton. Also, it is shown that a generalized Sasakian-space-form with 𝛽-Kenmotsu structure admitting a gradient Ricci-Bourguignon soliton is either ψ∖T^k × M^2n+1-k or gradient 𝜂-Yamabe soliton.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.847-863
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• 2020

The aim of the present paper is to study some solitons on three dimensional generalized (𝜅, 𝜇)-contact metric manifolds. We study gradient Yamabe solitons on three dimensional generalized (𝜅, 𝜇)-contact metric manifolds. It is proved that if the metric of a three dimensional generalized (𝜅, 𝜇)-contact metric manifold is gradient Einstein soliton then ${\mu}={\frac{2{\kappa}}{{\kappa}-2}}$. It is shown that if the metric of a three dimensional generalized (𝜅, 𝜇)-contact metric manifold is closed m-quasi Einstein metric then ${\kappa}={\frac{\lambda}{m+2}}$ and 𝜇 = 0. We also study conformal gradient Ricci solitons on three dimensional generalized (𝜅, 𝜇)-contact metric manifolds.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.613-623
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• 2020

The notion of quasi-Einstein metric in theoretical physics and in relation with string theory is equivalent to the notion of Ricci soliton in differential geometry. Quasi-Einstein metrics or Ricci solitons serve also as solution to Ricci flow equation, which is an evolution equation for Riemannian metrics on a Riemannian manifold. Quasi-Einstein metrics are subject of great interest in both mathematics and theoretical physics. In this paper the notion of Ricci 𝜌-soliton as a generalization of Ricci soliton is defined. We are motivated by the Ricci-Bourguignon flow to define this concept. We show that if a 3-dimensional almost Kenmotsu Einstein manifold M is a 𝜌-soliton, then M is a Kenmotsu manifold of constant sectional curvature -1 and the 𝜌-soliton is expanding with λ = 2.