Gradient Ricci solitons with a conformal vector field

Abstract

We show that a connected gradient Ricci soliton ( $$M,g,f,\lambda $$ ) with constant scalar curvature and admitting a non-homothetic conformal vector field V leaving the potential vector field invariant, is Einstein and the potential function f is constant. For locally conformally flat case and non-homothetic V we show without constant scalar curvature assumption, that f is constant and g has constant curvature.