Paper · May 20, 2026
Complete gradient Ricci solitons with zero radial Weyl curvature
As on arXiv
Abstract
In this paper, we study the complete gradient Ricci solitons with zero radial Weyl curvature, which means that the interior product of with the Weyl tensor is zero, i.e., . We classify completely the complete gradient Ricci solitons with zero radial Weyl curvature for the dimension .
- Submitted
- May 20, 2026
- Last revised
- Jul 7, 2026 (v2)
- Subjects
- math.DG
Comments: There is a calculation error in the paper
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Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 11B.1Ricci Solitons
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.
- 12B.2The Asymptotic Soliton and Three-Dimensional Shrinkers
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.