English

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

Differential Geometry 2026-03-17 v2

Abstract

We construct a continuous 3-parameter family of non-shrinking Ricci solitons complex line bundles O(k)O(k) over CP2m+1\mathbb{CP}^{2m+1}, where the base space is not necessarily K\"ahler--Einstein. Each O(k)O(k) with k[3,2m+1]k\in [3,2m+1] admits at least one asymptotically conical (AC) Ricci-flat metric in this family. For each O(k)O(k) with k3k\geq 3, the family includes infinitely many asymptotically paraboloidal (AP) steady Ricci soliton.

Keywords

Cite

@article{arxiv.2412.16907,
  title  = {Infinitely many non-collapsed steady Ricci solitons on complex line bundles},
  author = {Hanci Chi},
  journal= {arXiv preprint arXiv:2412.16907},
  year   = {2026}
}

Comments

Citations added. Typos fixed