Rigidity of gradient Einstein shrinkers

In this paper, we consider a perturbation of the Ricci solitons equation proposed in [J.-P. Bourguignon, Ricci curvature and Einstein metrics, in Global Differential Geometry and Global Analysis, Lecture Notes in Mathematics, Vol. 838 (Springer, Berlin, 1981), pp. 42–63] and studied in [H.-D. Cao, Geometry of Ricci solitons, Chinese Ann. Math. Ser. B27(2) (2006) 121–142] and we classify noncompact gradient shrinkers with bounded non-negative sectional curvature.