• Kyungpook Mathematical Journal
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• 제57권2호
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• pp.309-318
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• 2017

The object of the present paper is to study almost Ricci solitons and gradient almost Ricci solitons in 3-dimensional f-Kenmotsu manifolds.

• 대한수학회지
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• 제57권2호
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• pp.539-552
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• 2020

In this paper we consider gradient almost Ricci solitons with weak conditions on Weyl and Bach tensors. We show that a gradient almost Ricci soliton has harmonic Weyl curvature if it has fourth order divergence-free Weyl tensor, or it has divergence-free Bach tensor. Furthermore, if its Weyl tensor is radially flat, we prove such a gradient almost Ricci soliton is locally a warped product with Einstein fibers. Finally, we prove a rigidity result on compact gradient almost Ricci solitons satisfying an integral condition.

• 대한수학회지
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• 제55권1호
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• pp.161-174
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• 2018

The aim of this article is to study the k-almost Ricci soliton and k-almost gradient Ricci soliton on contact metric manifold. First, we prove that if a compact K-contact metric is a k-almost gradient Ricci soliton, then it is isometric to a unit sphere $S^{2n+1}$. Next, we extend this result on a compact k-almost Ricci soliton when the flow vector field X is contact. Finally, we study some special types of k-almost Ricci solitons where the potential vector field X is point wise collinear with the Reeb vector field ${\xi}$ of the contact metric structure.

• 대한수학회지
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• 제53권5호
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• pp.1101-1114
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• 2016

Let ($M^{2n+1}$, ${\phi}$, ${\xi}$, ${\eta}$, g) be a (k, ${\mu}$)'-almost Kenmotsu manifold with k < -1 which admits a gradient Ricci almost soliton (g, f, ${\lambda}$), where ${\lambda}$ is the soliton function and f is the potential function. In this paper, it is proved that ${\lambda}$ is a constant and this implies that $M^{2n+1}$ is locally isometric to a rigid gradient Ricci soliton ${\mathbb{H}}^{n+1}(-4){\times}{\mathbb{R}}^n$, and the soliton is expanding with ${\lambda}=-4n$. Moreover, if a three dimensional Kenmotsu manifold admits a gradient Ricci almost soliton, then either it is of constant sectional curvature -1 or the potential vector field is pointwise colinear with the Reeb vector field.

• Kyungpook Mathematical Journal
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• 제63권4호
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• pp.623-638
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• 2023

In this article we study a 𝛿-Ricci-Yamabe almost soliton within the framework of paracontact metric manifolds. In particular we study 𝛿-Ricci-Yamabe almost soliton and gradient 𝛿-Ricci-Yamabe almost soliton on K-paracontact and para-Sasakian manifolds. We prove that if a K-paracontact metric g represents a 𝛿-Ricci-Yamabe almost soliton with the non-zero potential vector field V parallel to 𝜉, then g is Einstein with Einstein constant -2n. We also show that there are no para-Sasakian manifolds that admit a gradient 𝛿-Ricci-Yamabe almost soliton. We demonstrate a 𝛿-Ricci-Yamabe almost soliton on a (𝜅, 𝜇)-paracontact manifold.

• Korean Journal of Mathematics
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• 제27권3호
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• pp.691-705
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• 2019

In the present paper is to classify Beta-almost (${\beta}$-almost) Ricci solitons and ${\beta}$-almost gradient Ricci solitons on almost $CoK{\ddot{a}}hler$ manifolds with ${\xi}$ belongs to ($k,{\mu}$)-nullity distribution. In this paper, we prove that such manifolds with V is contact vector field and $Q{\phi}={\phi}Q$ is ${\eta}$-Einstein and it is steady when the potential vector field is pointwise collinear to the reeb vectoer field. Moreover, we prove that a ($k,{\mu}$)-almost $CoK{\ddot{a}}hler$ manifolds admitting ${\beta}$-almost gradient Ricci solitons is isometric to a sphere.

• 대한수학회지
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• 제60권2호
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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.