*-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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A classification of certain almost α-Kenmotsu manifolds
TL;DR: In this paper, the authors characterize almost contact metric manifolds which are CR-integrable almost α-Kenmotsu manifolds, through the existence of a canonical linear connection, invariant under $\mathscr{D}$-homothetic deformations.
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-Ricci Solitons on Sasakian 3-Manifolds
TL;DR: In this paper, a Ricci tensor tensor of Codazzi type and cyclic parallel tensor has been considered on Sasakian 3-manifolds with curvature condition Q.R = 0 and conformally flat and φ-Ricci symmetric Ricci solitons.
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Some results on (k, μ)′-almost Kenmotsu manifolds
Yaning Wang,Wenjie Wang +1 more
TL;DR: In this paper, the Weyl conformal curvature tensor and concircular curvatures tensor were studied on a (k, μ)′-almost Kenmotsu manifold M2n+1 of dimension greater than 3.
Some results on almost Kenmotsu manifolds
TL;DR: In this article, it was shown that for a -almost-Kenmotsu manifold with and, the tensor vanishes and every conformal vector field which leaves the curvature tensor invariant is Killing.
SOME RESULTS ON (k, µ)'-ALMOST KENMOTSU MANIFOLDS
Wenfeng Ning,Ximin Liu,Jin Li +2 more
TL;DR: In this paper, the quasi-conformal curvature tensor C and projective tensor P on a (k, µ)-almost Kenmotsu manifold M 2 n + 1 of dimension greater than 3 were studied.