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arXiv · 2506.11362

Expanding Ricci solitons and Higgs bundles

Ramiro A. Lafuente·Adam Thompson
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Abstract

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.

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Ramiro A. Lafuente, Adam Thompson. 2025-06-12. Expanding Ricci solitons and Higgs bundles. https://arxiv.org/abs/2506.11362

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