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.
@article{33027,
title = {Ricci almost solitons and gradient Ricci almost solitons in $(k,\mu)$-paracontact geometry},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {37},
year = {2017},
doi = {10.5269/bspm.v37i3.33027},
language = {EN},
url = {http://dml.mathdoc.fr/item/33027}
}
De, Uday Chand; Mandal, Krishanu. Ricci almost solitons and gradient Ricci almost solitons in $(k,\mu)$-paracontact geometry. Boletim da Sociedade Paranaense de Matemática, Tome 37 (2017) . doi : 10.5269/bspm.v37i3.33027. http://gdmltest.u-ga.fr/item/33027/