  We define a gradient Ricci soliton to be rigid if it is a flat bundle $%
N\times_{\Gamma}\mathbb{R}^{k}$ where $N$ is Einstein. It is known that not all
gradient solitons are rigid. Here we offer several natural conditions on the
curvature that characterize rigid gradient solitons. Other related results on
rigidity of Ricci solitons are also explained in the last section.
