*-Ricci soliton on (κ, μ)′-almost Kenmotsu manifolds
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In this article, it was shown that if the metric g of M is a *-Ricci soliton, then either M is locally isometric to the product ℍn+1(−4)×ℝn or the potential vector field is strict infinitesimal contact transformation.Abstract:
Abstract Let (M, g) be a non-Kenmotsu (κ, μ)′-almost Kenmotsu manifold of dimension 2n + 1. In this paper, we prove that if the metric g of M is a *-Ricci soliton, then either M is locally isometric to the product ℍn+1(−4)×ℝn or the potential vector field is strict infinitesimal contact transformation. Moreover, two concrete examples of (κ, μ)′-almost Kenmotsu 3-manifolds admitting a Killing vector field and strict infinitesimal contact transformation are given.read more
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$$*$$ ∗ - $$\eta $$ η -Ricci soliton and contact geometry
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Almost Kenmotsu $$(k,\mu )'$$ ( k , μ ) ′ -manifolds with Yamabe solitons
TL;DR: In this article, it was shown that if the metric g represents a Yamabe soliton, then it is locally isometric to the product space and the contact transformation is a strict infinitesimal contact transformation.
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Non-existence of $$*$$ ∗ -Ricci solitons on $$(\kappa ,\mu )$$ ( κ , μ ) -almost cosymplectic manifolds
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Certain types of metrics on almost coKähler manifolds
TL;DR: In this article, it was shown that Bach flat almost coKahler manifold admits Ricci solitons, satisfying the critical point equation (CPE) or Bach flat.
References
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Contact 3-manifolds and $*$-Ricci soliton
TL;DR: In this article, it was shown that the Ricci soliton of a 3-dimensional Kenmotsu manifold is locally isometric to the hyperbolic 3-space and the potential vector field coincides with the Reeb vector field.
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K-contact metrics as Ricci solitons
Amalendu Ghosh,Ramesh Sharma +1 more
TL;DR: Ghosh et al. as mentioned in this paper studied Ricci solitons on a Riemannian manifold whose metric is a Ricci tensor and showed that Ricci is a generalization of the Einstein metric and is defined on the manifold by ( £ V g) + 2 S(X,Y) +2 R ij projected from the space of metrics onto its quotient modulodiffeomorphisms and scalings.
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Ricci solitons and contact metric manifolds
TL;DR: In this article, a Ricci soliton with potential vector field V collinear with ξ at each point under different curvature conditions was studied on a contact metric manifold M2n+1(ϕ, ξ, η, g).
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Ricci solitons on almost Kenmotsu 3-manifolds
TL;DR: In this article, it was shown that if g represents a Ricci soliton whose potential vector field is orthogonal to the Reeb vector field, then M3 is locally isometric to either the hyperbolic space ℍ3(−1) or a non-unimodular Lie group equipped with a left invariant non-Kenmotsu almost Kenmotsusu structure.
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