Abstract: By using the existing rigidity theorem of gradient Ricci solitons, we discussed complete non-compact gradient expanding Riccisolitons. Under the conditions that the Ricci curvature was non-negative, the radial curvature vanished and the fourth order divergence of the Weyl tensor was non-negative, we obtained its rigidity result.

Key words: gradient expanding Ricci soliton, rigidity, radial curvature, Weyl tensor