Quasi Yamabe Solitons on 3-Dimensional Contact Metric Manifolds with Qφ=φQ
In this paper we initiate the study of quasi Yamabe soliton on 3-dimensional contact metric manifold with Qφ=φQ and prove that if a 3-dimensional contact metric manifold M such that Qφ=φQ admits a quasi Yamabe soliton with non-zero soliton vector field V being point-wise collinear with the Reeb vector field ξ, then V is a constant multiple of ξ, 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 Qφ=φQ endowed with a quasi Yamabe soliton, then either M is flat or soliton is trivial.
math.DG↗