On Yamabe Soliton

Abstract

The purpose of the paper is to prove that if the metric of a 3-dimensional α-Sasakian structure on a complete Riemannian manifold is a Yamabe soliton then it is of constant curvature. We also derive some properties of the flow vector field U of the Yamabe soliton together with an example of an α-Sasakian manifold admitting Yamabe soliton.