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Steady conformally Kähler Ricci solitons with isoparametric potential
Abstract
We classify complete, non-compact, simply connected, irreducible four-dimensional steady gradient Ricci solitons that are globally conformally Kähler and have an isoparametric potential. The steady Ricci solitons are U(2)-invariant nuts on ℝ4, including the Bryant and Cao solitons, and bolts on 𝕊2 × ℝ2 and on 𝒪(−m)→ℂℙ1. For each m≥3 there is exactly one non-collapsed bolt. A key step, valid for Ricci solitons of every sign, is that away from the locally conformally flat case, the conformal factor is aligned with the potential function, which yields cohomogeneity-one symmetry.
Related
- Linear Stability of Steady and Expanding Kähler-Ricci Solitons
- Instability of conformally Kähler, Einstein metrics
- On products of locally conformally Kähler manifolds
- Scalar and tensor eigenvalue bounds for conformally Kähler Einstein four-manifolds
- Extremal Kähler--Ricci solitons on Fano manifolds are Kähler--Einstein
BibTeX
@misc{jr2026steady,
title = {{Steady conformally Kähler Ricci solitons with isoparametric potential}},
author = {Ernani Ribeiro Jr and Hung Tran},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40994},
eprint = {2610.40994},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40994},
}
RIS
TY - UNPB
TI - Steady conformally Kähler Ricci solitons with isoparametric potential
AU - Ernani Ribeiro Jr
AU - Hung Tran
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40994
UR - https://arxiv.org/abs/2610.40994
AB - We classify complete, non-compact, simply connected, irreducible four-dimensional steady gradient Ricci solitons that are globally conformally Kähler and have an isoparametric potential. The steady Ricci solitons are U(2)-invariant nuts on ℝ^4, including the Bryant and Cao solitons, and bolts on 𝕊^2 × ℝ^2 and on 𝒪(−m)→ℂℙ^1. For each m≥3 there is exactly one non-collapsed bolt. A key step, valid for Ricci solitons of every sign, is that away from the locally conformally flat case, the conformal factor is aligned with the potential function, which yields cohomogeneity-one symmetry.
ER -