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Let (M, g) be a steady gradient Ricci soliton of dimension n 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 -noncollapsed and have positive isotropic curvature.
Simon Brendle (Sun,) studied this question.