  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
result applies to steady gradient Ricci solitons in dimension 4 which are
\kappa-noncollapsed and have positive isotropic curvature.
