ricci almost solitons and gradient ricci almost solitons in $(k,\mu)$-paracontact geometry

ricci almost solitons and gradient ricci almost solitons in $(k,\mu)$-paracontact geometry

;Uday Chand De;Krishanu Mandal
urban geography 2019 Vol. 37 pp. 119-130
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de2019boletimricci

Abstract

The purpose of this paper is to study Ricci almost soliton and gradient Ricci almost soliton in $(k,\mu)$-paracontact metric manifolds. We prove the non-existence of Ricci almost soliton in a $(k,\mu)$-paracontact metric manifold $M$ with $k<-1$ or $k>-1$ and whose potential vector field is the Reeb vector field $\xi$. Further, if the metric $g$ of a $(k,\mu)$-paracontact metric manifold $M^{2n+1}$ with $k\neq-1$ is a gradient Ricci almost soliton, then we prove either the manifold is locally isometric to a product of a flat $(n+1)$-dimensional manifold and an $n$-dimensional manifold of negative constant curvature equal to $-4$, or, $M^{2n+1}$ is an Einstein manifold.

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