Ricci Almost Solitons on Three-Dimensional Quasi-Sasakian Manifolds

Abstract

In this paper it is shown that a three-dimensional non-cosymplectic quasi-Sasakian manifold admitting Ricci almost soliton is locally $$\phi $$-symmetric. It is proved that a Ricci almost soliton on a three-dimensional quasi-Sasakian manifold reduces to a Ricci soliton. It is also proved that if a three-dimensional non-cosymplectic quasi-Sasakian manifold admits gradient Ricci soliton, then the potential function is invariant in the orthogonal distribution of the Reeb vector field $$\xi$$. We also improve some previous results regarding gradient Ricci soliton on three-dimensional quasi-Sasakian manifolds. An illustrative example is given to support the obtained results.