Classification of cohomogeneity one steady gradient Ricci solitons in dimension four and five

Abstract

In this paper, we first prove Appleton's conjecuture on the uniqueness of noncollapsed steady solitons constructed in \cite{Appleton}. We also classify non-Ricci-flat $\kappa$-noncollapsed cohomogeneity one steady gradient Ricci solitons in dimension four and five. After passing to a finite cover, in dimension four, they must be the Bryant soliton or Appleton's noncollapsed 4d steady soliton; in dimension five, they must be the Bryant soliton or solitons constructed by Ivey--Dancer--Wang.

arXiv comment57 pages