Yamabe solitons and gradient Yamabe solitons on three-dimensional N(k)-contact manifolds.

If a three-dimensional N (k) -contact metric manifold M admits a Yamabe soliton of type (M , g , V) , then the manifold has a constant scalar curvature and the flow vector field V is Killing. Furthermore, either M has a constant curvature k or the flow vector field V is a strict contact infinitesimal transformation. Also, we prove that if the metric of a three-dimensional N (k) -contact metric manifold M admits a gradient Yamabe soliton, then either the manifold is flat or the scalar curvature is constant. Moreover, either the potential function is constant or the manifold is of constant sectional curvature k. Finally, we have given an example to verify our result. [ABSTRACT FROM AUTHOR]