Ricci almost solitons and gradient Ricci almost solitons in $(k,μ)$-paracontact geometry - Uday Chand De; Krishanu Mandal (Boletim da Sociedade Paranaense de Matemática, 2019)
The purpose of this paper is to study Ricci almost soliton and gradient Ricci almost soliton in $(k,μ)$-paracontact metric manifolds. We prove the non-existence of Ricci almost soliton in a $(k,μ)$-paracontact metric manifold $M$ with $k<-1$ or $k>-1$ and whose potential vector field is the Reeb vector field $ξ$. Further, if the metric $g$ of a $(k,μ)$-paracontact metric manifold $M^{2n+1}$ with $k≠-1$ 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.