$O(3)$-symmetry of four-dimensional steady Ricci solitons

We prove that a complete connected four-dimensional gradient steady Ricci soliton with positive curvature operator that is $κ$-noncollapsed at all scales admits an effective isometric $O(3)$ action preserving the potential function and having principal orbits diffeomorphic to $S^2$.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-27
DOI
https://doi.org/10.48550/arxiv.2610.36563
Primary Topic
Geometric Analysis and Curvature Flows
Type
preprint
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preprint

$O(3)$-symmetry of four-dimensional steady Ricci solitons

Hanbing Fang
arXiv (Cornell University)
Geometric Analysis and Curvature Flows
preprint

$O(3)$-symmetry of four-dimensional steady Ricci solitons

Hanbing Fang
preprint en

Abstract

We prove that a complete connected four-dimensional gradient steady Ricci soliton with positive curvature operator that is $κ$-noncollapsed at all scales admits an effective isometric $O(3)$ action preserving the potential function and having principal orbits diffeomorphic to $S^2$.

arXiv (Cornell University)
Geometric Analysis and Curvature Flows
DOIOpen Access PDFOpenAlex
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$O(3)$-symmetry of four-dimensional steady Ricci solitons — Hanbing Fang · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS