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

Abstract

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 nonexistence 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 that 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. Finally, an illustrative example is given.