A note on the classification of four-dimensional gradient steady and expanding Ricci solitons
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911552186089472 |
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| author | Cao, Huai-Dong Xie, Junming |
| author_facet | Cao, Huai-Dong Xie, Junming |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27793 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A note on the classification of four-dimensional gradient steady and expanding Ricci solitons Cao, Huai-Dong Xie, Junming Differential Geometry 53C25, 53C21, 53E20 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. |
| title | A note on the classification of four-dimensional gradient steady and expanding Ricci solitons |
| topic | Differential Geometry 53C25, 53C21, 53E20 |
| url | https://arxiv.org/abs/2603.27793 |