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. 
Pengfei Guan, Peng Lu and Yiyan Xu
math.DG math.AP