Infinitely many non-collapsed steady Ricci solitons on complex line bundles

Abstract

We construct a continuous 3-parameter family of non-shrinking Ricci solitons complex line bundles $O(k)$ over ${\mathbb{CP}}^{2m+1}$, where the base space is not necessarily Kähler--Einstein. Each $O(k)$ with $k\in [3,2m+1]$ admits at least one asymptotically conical (AC) Ricci-flat metric in this family. For each $O(k)$ with $k\ge 3$, the family includes infinitely many asymptotically paraboloidal (AP) steady Ricci soliton.

arXiv commentTypos fixed. Section 5 has been restructured for better exposition