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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.11362 |
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| _version_ | 1866911287949131776 |
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| author | Lafuente, Ramiro A. Thompson, Adam |
| author_facet | Lafuente, Ramiro A. Thompson, Adam |
| contents | Motivated by the long-time behavior of Ricci flows that collapse with bounded curvature, we study expanding Ricci solitons with nilpotent symmetry on vector bundles over a closed manifold. We prove that, under mild assumptions that are satisfied by Ricci flow limits, the equations dimension-reduce to the so-called twisted harmonic-Einstein equations. When the base is a surface, we establish a correspondence between solutions of the latter and a class of G-Higgs bundles. This allows us to produce infinite families of new examples that are not locally homogeneous, and in particular to obtain a complete description in dimension 4. We also show that all our examples admit Einstein one-dimensional extensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11362 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Expanding Ricci solitons and Higgs bundles Lafuente, Ramiro A. Thompson, Adam Differential Geometry 53C25, 53C07 Motivated by the long-time behavior of Ricci flows that collapse with bounded curvature, we study expanding Ricci solitons with nilpotent symmetry on vector bundles over a closed manifold. We prove that, under mild assumptions that are satisfied by Ricci flow limits, the equations dimension-reduce to the so-called twisted harmonic-Einstein equations. When the base is a surface, we establish a correspondence between solutions of the latter and a class of G-Higgs bundles. This allows us to produce infinite families of new examples that are not locally homogeneous, and in particular to obtain a complete description in dimension 4. We also show that all our examples admit Einstein one-dimensional extensions. |
| title | Expanding Ricci solitons and Higgs bundles |
| topic | Differential Geometry 53C25, 53C07 |
| url | https://arxiv.org/abs/2506.11362 |