Rotational symmetry of Ricci solitons in higher dimensions

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.