*-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
More filters
Journal ArticleDOI
$$*$$ ∗ - $$\eta $$ 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.
Journal ArticleDOI
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.
Journal ArticleDOI
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.
Journal ArticleDOI
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
More filters
Journal ArticleDOI
Real Hypersurfaces of Complex Space Forms in Terms of Ricci $*$-Tensor
TL;DR: In this article, the authors classified the $*$-Einstein real hypersurfaces in complex space forms such that the structure vector is a principal curvature vector and the principal curvatures of the hypersurface can be computed with the K\"ahler metric.
Journal ArticleDOI
*-Ricci solitons of real hypersurfaces in non-flat complex space forms
TL;DR: In this paper, the notion of *-Ricci soliton is introduced and real hypersurfaces in non-flat complex space forms admitting a *-ricci s soliton with potential vector field being the structure vector field.
Journal ArticleDOI
Kenmotsu 3-metric as a Ricci soliton
TL;DR: In this paper, it was shown that if a 3D Kenmotsu metric is a Ricci soliton, then it is of constant curvature −1 and the soliton is expanding.
Journal ArticleDOI
Contact geometry and ricci solitons
Jong Taek Cho,Ramesh Sharma +1 more
TL;DR: In this article, a compact contact Ricci soliton with a potential vector field V collinear with the Reeb vector field, is shown to be the equivalent of an Eigenvector.