Dibakar Dey

Bio: Dibakar Dey is an academic researcher from University of Calcutta. The author has contributed to research in topics: Manifold & Einstein manifold. The author has an hindex of 4, co-authored 21 publications receiving 39 citations.

Almost Kenmotsu metric as a conformal Ricci soliton

Abstract:

In the present paper, we characterize ( k , μ ) ′ (k,\mu )’ and generalized ( k , μ ) ′ (k,\mu )’ -almost Kenmotsu manifolds admitting the conformal Ricci soliton. It is also shown that a ( k , μ ) ′ (k,\mu )’ -almost Kenmotsu manifold M 2 n + 1 M^{2n+1} does not admit conformal gradient Ricci soliton ( g , V , λ ) (g,V,\lambda ) with V V collinear with the characteristic vector field ξ \xi . Finally an illustrative example is presented.

Pseudo-symmetric structures on almost Kenmotsu manifolds with nullity distributions

Abstract: The object of the present paper is to characterize Ricci pseudosymmetric and Ricci semisymmetric almost Kenmotsu manifolds with (k; μ)-, (k; μ)′-, and generalized (k; μ)-nullity distributions. We also characterize (k; μ)-almost Kenmotsu manifolds satisfying the condition R ⋅ S = LꜱQ(g; S2).

Almost Kenmotsu metric as quasi Yamabe soliton

Abstract: The object of the present paper is to characterize two classes of almost Kenmotsu manifolds admitting Ricci-Yamabe soliton. It is shown that a $(k,\mu)'$-almost Kenmotsu manifold admitting a Ricci-Yamabe soliton or gradient Ricci-Yamabe soliton is locally isometric to the Riemannian product $\mathbb{H}^{n+1}(-4) \times \mathbb{R}^n$. For the later case, the potential vector field is pointwise collinear with the Reeb vector field. Also, a $(k,\mu)$-almost Kenmotsu manifold admitting certain Ricci-Yamabe soliton with the curvature property $Q \cdot P = 0$ is locally isometric to the hyperbolic space $\mathbb{H}^{2n+1}(-1)$ and the non-existense of the curvature property $Q \cdot R = 0$ is proved.

Critical point equation on a class of almost Kenmotsu manifolds

Abstract: In the present paper, we characterize $$(k,\mu )'$$-almost Kenmotsu manifolds admitting $$*$$-critical point equation. It is shown that if $$(g, \lambda )$$ is a non-constant solution of the $$*$$-critical point equation of a connected non-compact $$(k,\mu )'$$-almost Kenmotsu manifold, then (1) the manifold M is locally isometric to $$\mathbb {H}^{n+1}(-4)$$$$\times $$$$\mathbb {R}^n$$, (2) the manifold M is $$*$$-Ricci flat and (3) the function $$\lambda $$ is harmonic. Finally an illustrative example is presented.

On Ricci–Yamabe soliton and geometrical structure in a perfect fluid spacetime

Abstract: In this paper, we studied the geometrical aspects of a perfect fluid spacetime with torse-forming vector field $$\xi $$ under certain curvature restrictions, and Ricci–Yamabe soliton and $$\eta $$ -Ricci–Yamabe soliton in a perfect fluid spacetime. Conditions for the Ricci–Yamabe soliton to be steady, expanding or shrinking are also given. Moreover, when the potential vector field $$\xi $$ of $$\eta $$ -Ricci–Yamabe soliton is of gradient type, we derive a Poisson equation and also looked at its particular cases. Lastly, a non-trivial example of perfect fluid spacetime admitting $$\eta $$ -Ricci–Yamabe soliton is constructed.

Almost Kenmotsu metric as quasi Yamabe soliton

Abstract: The object of the present paper is to characterize two classes of almost Kenmotsu manifolds admitting Ricci-Yamabe soliton. It is shown that a $(k,\mu)'$-almost Kenmotsu manifold admitting a Ricci-Yamabe soliton or gradient Ricci-Yamabe soliton is locally isometric to the Riemannian product $\mathbb{H}^{n+1}(-4) \times \mathbb{R}^n$. For the later case, the potential vector field is pointwise collinear with the Reeb vector field. Also, a $(k,\mu)$-almost Kenmotsu manifold admitting certain Ricci-Yamabe soliton with the curvature property $Q \cdot P = 0$ is locally isometric to the hyperbolic space $\mathbb{H}^{2n+1}(-1)$ and the non-existense of the curvature property $Q \cdot R = 0$ is proved.