English

A note on the classification of four-dimensional gradient steady and expanding Ricci solitons

Differential Geometry 2026-03-31 v1

Abstract

In this note, we study the classification of four-dimensional complete gradient steady and expanding Ricci solitons. Specifically, under the asymptotically cylindrical (respectively, asymptotically conical) assumption, we classify gradient steady (respectively, expanding) Ricci solitons with half-harmonic Weyl curvature. In addition, we obtain a partial classification of four-dimensional gradient expanding Ricci solitons with half-nonnegative isotropic curvature.

Keywords

Cite

@article{arxiv.2603.27793,
  title  = {A note on the classification of four-dimensional gradient steady and expanding Ricci solitons},
  author = {Huai-Dong Cao and Junming Xie},
  journal= {arXiv preprint arXiv:2603.27793},
  year   = {2026}
}

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11 pages