A Family of Steady Ricci Solitons and Ricci-flat Metrics

Abstract

We produce new non-Kähler 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 $\mathrm{Sp}(1)$ bundles over quaternionic projective space.

25 pages, 9 figures, corollary regarding differential structures added