Cohomogeneity one Ricci Solitons from Hopf Fibrations

This paper studies cohomogeneity one Ricci solitons. If the isotropy representation of the principal orbit $G\mathrm{/}K$ consists of two inequivalent $A{d}_K$-invariant irreducible summands, the existence of parameter families of non-homothetic complete steady and expanding Ricci solitons on non-trivial bundles is shown. These examples were detected numerically by Buzano-Dancer-Gallaugher-Wang. The analysis of the corresponding Ricci flat trajectories is used to reconstruct Einstein metrics of positive scalar curvature due to B"ohm. The techniques also apply to $m$-quasi-Einstein metrics.