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

TL;DR

This paper constructs a family of non-shrinking Ricci solitons on complex line bundles over projective spaces, revealing infinitely many steady Ricci solitons with specific asymptotic behaviors.

Contribution

It introduces a new continuous family of Ricci solitons on complex line bundles over non-Kähler bases, including infinitely many steady solitons with asymptotic paraboloidal geometry.

Findings

Existence of a 3-parameter family of Ricci solitons on $O(k)$ over $ ext{CP}^{2m+1}$

Presence of infinitely many steady Ricci solitons with asymptotically paraboloidal geometry

Construction of Ricci-flat metrics asymptotically conical on these 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 K\"ahler--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 $k\geq 3$, the family includes infinitely many asymptotically paraboloidal (AP) steady Ricci soliton.