A Family of Steady Ricci Solitons and Ricci-flat Metrics

We produce new non-K"ahler complete steady gradient Ricci solitons whose asymptotics combine those of the Bryant solitons and the Hamilton cigar. We also obtain a family of complete Ricci-flat metrics with asymptotically locally conical asymptotics. Finally, we obtain numerical evidence for complete steady soliton structures on the vector bundles whose distance sphere bundles are respectively the twistor and $\mathrm{S}\mathrm{p}(1)$ bundles over quaternionic projective space.