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

Abstract

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.

arXiv comment17 pages

References in corpus (4)

• Ricci flow with surgery on three-manifolds
• A Microscopic Convexity Principle for Nonlinear Partial Differential Equations
• A compactness theorem for complete Ricci shrinkers
• On shrinking Gradient Ricci Soliton With Nonnegative Sectional Curvature