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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.
Almost Ricci Soliton and Gradient Almost Ricci Soliton on 3-dimensional f-Kenmotsu Manifolds
Majhi, Pradip Department of Mathematics 2017 Kyungpook mathematical journal Vol.57 No.2
The object of the present paper is to study almost Ricci solitons and gradient almost Ricci solitons in 3-dimensional f-Kenmotsu manifolds.
On C-parallel Legendre and Magnetic curves in three dimensional Kenmotsu manifolds
Pradip Majhi,Changhwa Woo,Abhijit Biswas 한국전산응용수학회 2022 Journal of applied mathematics & informatics Vol.40 No.3
We find the characterizations of the curvatures of Legendre curves and magnetic curves in Kenmotsu manifolds with C-parallel and C-proper mean curvature vector fields in the tangent and normal bundles. Finally, an illustrative example is presented.
Some special curves in three dimensional f-Kenmotsu manifolds
Pradip Majhi,Abhijit Biswas 한국수학교육학회 2020 純粹 및 應用數學 Vol.27 No.2
In this paper we study Biharmonic curves, Legendre curves and Magnetic curves in three dimensional $f$-Kenmotsu manifolds. We also study $1$-type curves in a three dimensional $f$-Kenmotsu manifold by using the mean curvature vector field of the curve. As a consequence we obtain for a biharmonic helix in a three dimensional $f$-Kenmotsu manifold with the curvature $\kappa$ and the torsion $\tau$, $\kappa^{2} + \tau^{2} = -(f^{2} +f^{\prime})$. Also we prove that if a $1$-type non-geodesic biharmonic curve $\gamma$ is helix, then $\lambda = -(f^{2} + f').
Beta-almost Ricci solitons on almost CoKahler manifolds
Debabrata Kar,Pradip Majhi 강원경기수학회 2019 한국수학논문집 Vol.27 No.3
In the present paper is to classify Beta-almost ($\beta$-almost) Ricci solitons and $\beta$-almost gradient Ricci solitons on almost CoK\"ahler 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\"ahler manifolds admitting $\beta$-almost gradient Ricci solitons is isometric to a sphere.
On a Classification of Almost Kenmotsu Manifolds with Generalized (k, µ)'-nullity Distribution
Ghosh, Gopal,Majhi, Pradip,Chand De, Uday Department of Mathematics 2018 Kyungpook mathematical journal Vol.58 No.1
In the present paper we prove that in an almost Kenmotsu manifold with generalized $(k,{\mu})^{\prime}-nullity$ distribution the three conditions: (i) the Ricci tensor of $M^{2n+1}$ is of Codazzi type, (ii) the manifold $M^{2n+1}$ satisfies div C = 0, (iii) the manifold $M^{2n+1}$ is locally isometric to $H^{n+1}(-4){\times}R^n$, are equivalent. Also we prove that if the manifold satisfies the cyclic parallel Ricci tensor, then the manifold is locally isometric to $H^{n+1}(-4){\times}\mathbb{R}^n$.
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.
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.