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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.