Rigidity results for Riemann solitons

In this paper we take a look at conditions that make a Riemann soliton trivial, compacity being one of them. We also show that the behaviour at infinity of the gradient field of a non-compact gradient Riemann soliton might cause the soliton to be an Einstein manifold. Finally, we obtain scalar curvature estimates for complete shrinking or steady gradient Riemann solitons whose scalar curvature is bounded from below at infinity.