Calculus of Variations and Geometric Measure Theory
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G. Catino

Rigidity of positively curved shrinking Ricci solitons in dimension four

created by catino on 16 Jul 2018
modified on 28 Mar 2019


Accepted Paper

Inserted: 16 jul 2018
Last Updated: 28 mar 2019

Journal: Geom. Flows
Year: 2018


We classify four-dimensional shrinking Ricci solitons satisfying $Sec \geq \frac{1}{24} R$, 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.


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