Almost Ricci soliton and gradient almost Ricci soliton on 3-dimensional LP-Sasakian manifolds

Abstract

The object of the present paper is to study almost Ricci solitons and gradient almost Ricci solitons in 3-dimensional LP-Sasakian manifolds. We prove that if (g, V, λ) is an almost Ricci soliton on a 3-dimensional LP-Sasakian manifold M³, then it reduces to a Ricci soliton and the soliton is shrinking for λ=2. Furthermore, if the scalar curvature is constant on M³, then the potential vector field is Killing. Also, if the manifold admits a gradient almost Ricci soliton (f, ξ, λ), then the manifold is locally isometric to the unit sphere Sⁿ(1).