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∗-RICCI SOLITONS AND ∗-GRADIENT RICCI SOLITONS ON 3-DIMENSIONAL TRANS-SASAKIAN MANIFOLDS
Dey, Dibakar,Majhi, Pradip Korean Mathematical Society 2020 대한수학회논문집 Vol.35 No.2
The object of the present paper is to characterize 3-dimensional trans-Sasakian manifolds of type (α, β) admitting ∗-Ricci solitons and ∗-gradient Ricci solitons. Under certain restrictions on the smooth functions α and β, we have proved that a trans-Sasakian 3-manifold of type (α, β) admitting a ∗-Ricci soliton reduces to a β-Kenmotsu manifold and admitting a ∗-gradient Ricci soliton is either flat or ∗-Einstein or it becomes a β-Kenmotsu manifold. Also an illustrative example is presented to verify our results.
SASAKIAN 3-MANIFOLDS ADMITTING A GRADIENT RICCI-YAMABE SOLITON
Dey, Dibakar The Kangwon-Kyungki Mathematical Society 2021 한국수학논문집 Vol.29 No.3
The object of the present paper is to characterize Sasakian 3-manifolds admitting a gradient Ricci-Yamabe soliton. It is shown that a Sasakian 3-manifold M with constant scalar curvature admitting a proper gradient Ricci-Yamabe soliton is Einstein and locally isometric to a unit sphere. Also, the potential vector field is an infinitesimal automorphism of the contact metric structure. In addition, if M is complete, then it is compact.
Sasakian 3-Manifolds Satisfying Some Curvature Conditions Associated to Ƶ-Tensor
Dibakar Dey,Pradip Majhi 한국수학교육학회 2021 純粹 및 應用數學 Vol.28 No.2
In this paper, we study some curvature properties of Sasakian 3-manifolds associated to $\mathcal{Z}$-tensor. It is proved that if a Sasakian 3-manifold $(M,g)$ satisfies one of the conditions (1) the $\mathcal{Z}$-tensor is of Codazzi type, (2) $M$ is $\mathcal{Z}$-semisymmetric, (3) $M$ satisfies $Q(\mathcal{Z},R) = 0$, (4) $M$ is projectively $\mathcal{Z}$-semisymmetric, (5) $M$ is $\mathcal{Z}$-recurrent, then $(M,g)$ is of constant curvature 1. Several consequences are drawn from these results.
Sasakian 3-Metric as a $\ast$-Conformal Ricci Soliton Represents a Berger Sphere
Dibakar Dey 대한수학회 2022 대한수학회보 Vol.59 No.1
In this article, the notion of $\ast$-conformal Ricci soliton is defined as a self similar solution of the $\ast$-conformal Ricci flow. A Sasakian 3-metric satisfying the $\ast$-conformal Ricci soliton is completely classified under certain conditions on the soliton vector field. We establish a relation with Fano manifolds and proves a homothety between the Sasakian 3-metric and the Berger Sphere. Also, the potential vector field $V$ is a harmonic infinitesimal automorphism of the contact metric structure.
RICCI ρ-SOLITON IN A PERFECT FLUID SPACETIME WITH A GRADIENT VECTOR FIELD
Dibakar Dey,Pradip Majhi Korean Mathematical Society 2023 대한수학회논문집 Vol.38 No.1
In this paper, we studied several geometrical aspects of a perfect fluid spacetime admitting a Ricci ρ-soliton and an η-Ricci ρ-soliton. Beside this, we consider the velocity vector of the perfect fluid space time as a gradient vector and obtain some Poisson equations satisfied by the potential function of the gradient solitons.
Almost Kenmotsu Metrics with Quasi Yamabe Soliton
Pradip Majhi,Dibakar Dey 경북대학교 자연과학대학 수학과 2023 Kyungpook mathematical journal Vol.63 No.1
In the present paper, we characterize, for a class of almost Kenmotsu mani folds, those that admit quasi Yamabe solitons. We show that if a (k, µ)′ -almost Kenmotsu manifold admits a quasi Yamabe soliton (g, V, λ, α) where V is pointwise collinear with ξ, then (1) V is a constant multiple of ξ, (2) V is a strict infinitesimal contact transformation, and (3) (£V h′)X = 0 holds for any vector field X. We present an illustrative example to support the result.
On *-Conformal Ricci Solitons on a Class of Almost Kenmotsu Manifolds
Majhi, Pradip,Dey, Dibakar Department of Mathematics 2021 Kyungpook mathematical journal Vol.61 No.4
The goal of this paper is to characterize a class of almost Kenmotsu manifolds admitting *-conformal Ricci solitons. It is shown that if a (2n + 1)-dimensional (k, µ)'-almost Kenmotsu manifold M admits *-conformal Ricci soliton, then the manifold M is *-Ricci flat and locally isometric to ℍ<sup>n+1</sup>(-4) × ℝ<sup>n</sup>. The result is also verified by an example.