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

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