Quasi-einstein manifolds admitting conformal vector fields

We study an m-quasi-Einstein manifold (M, g, f, lambda) with finite m, and a non-homothetic conformal vector field U that leaves the potential vector field and the scalar curvature both invariant, and show that either M is trivial, or U is Killing on the set of regular points of f. In the case when M is a gradient Ricci soliton, it is trivial. Finally, for an m-quasi-Einstein manifold with finite m, and a homothetic vector field U leaving the potential vector field invariant, we show that either (i) M is Ricci-flat and f is constant, or (ii) U is Killing.