Rigidity of positively curved shrinking Ricci solitons in dimension four

Abstract

We classify four-dimensional shrinking Ricci solitons satisfying $Sec\ge \frac{1}{24}R$, where $Sec$ and $R$ denote the sectional and the scalar curvature, respectively. They are isometric to either ${\mathbb{R}}^4$ (and quotients), ${\mathbb{S}}^4$, ${\mathbb{RP}}^4$ or ${\mathbb{CP}}^2$ with their standard metrics.