Quasi Yamabe Solitons on 3-Dimensional Contact Metric Manifolds with Q\varphi=\varphi Q

Abstract

In this paper we initiate the study of quasi Yamabe soliton on 3-dimensional contact metric manifold with Q\varphi=\varphi Q and prove that if a 3-dimensional contact metric manifold M such that Q\varphi=\varphi Q admits a quasi Yamabe soliton with non-zero soliton vector field V being point-wise collinear with the Reeb vector field {\xi}, then V is a constant multiple of {\xi}, the scalar curvature is constant and the manifold is Sasakian. Moreover, V is Killing. Finally, we prove that if M is a 3-dimensional compact contact metric manifold such that Q\varphi=\varphi Q endowed with a quasi Yamabe soliton, then either M is flat or soliton is trivial.