*-Ricci soliton on (κ, μ)′-almost Kenmotsu manifolds
TLDR
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
Citations
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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
TL;DR: In this paper, the authors prove a non-existence result for Ricci solitons on non-cosymplectic manifolds, and prove the same result for almost cosympelous 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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∗-Ricci Soliton within the frame-work of Sasakian and (κ,μ)-contact manifold
TL;DR: In this article, it was shown that if a complete Sasakian metric is an almost gradient ∗-Ricci soliton, then it is either positive or null-Sakian.
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Ricci Solitons in -Sasakian Manifolds
TL;DR: It is shown that a symmetric parallel second order-covariant tensor in a 𝛼-Sasakian manifold is a constant multiple of the metric tensor.
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RICCI SOLITONS ON THREE-DIMENSIONAL $\eta$-EINSTEIN ALMOST KENMOTSU MANIFOLDS
Yaning Wang,Ximin Liu +1 more
TL;DR: In this article, it was shown that the Ricci soliton of a three-dimensional (3D)-Einstein almost-Einstein soliton is a Ricci manifold of constant sectional curvature.
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Almost Kenmotsu manifolds with conformal Reeb foliation
TL;DR: In this paper, the authors consider almost Kenmotsu manifolds with conformal Reeb foliation and prove that such a foliation produces harmonic morphisms, study the $k$-nullity distributions and discuss the isometrical immersion of such a manifold as hypersurface in a real space form of constant curvature.