A rigidity theorem for codimension one shrinking gradient Ricci solitons in ${\mathbb{R}}^{n+1}$

We prove a splitting theorem for complete gradient Ricci soliton with nonnegative curvature and establish a rigidity theorem for codimension one complete shrinking gradient Ricci soliton in ${\mathbb{R}}^{n+1}$ with nonnegative Ricci curvature.