Abstract
Let $(M, g)$ be a steady gradient Ricci soliton of dimension $n \geq 4$ which has positive sectional curvature and is asymptotically cylindrical. Under these assumptions, we show that $(M, g)$ is rotationally symmetric. In particular, our results apply to steady gradient Ricci solitons in dimension $4$ which are $\kappa$-noncollapsed and have positive isotropic curvature.
Citation
Simon Brendle. "Rotational symmetry of Ricci solitons in higher dimensions." J. Differential Geom. 97 (2) 191 - 214, June 2014. https://doi.org/10.4310/jdg/1405447804
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