*-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
TL;DR: In this article, the Ricci soliton is shown to be Ricci flat and locally isometric with respect to the Euclidean distance of the potential vector field when the manifold satisfies gradient almost.
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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.
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TL;DR: In this paper, a Ricci soliton with the Reeb potential vector field or a transversal vector field is of constant sectional curvature 0.1 and a cosymplectic 3-manifold admits Ricci s solitons of constant curvature -1.
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An \eta-Einstein Kenmotsu metric as a Ricci soliton
TL;DR: In this article, it was shown that if the metric of an η-Einstein Kenmotsu manifold is a Ricci soliton, then it is Einstein and the soliton is expanding.