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

Abstract

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