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arXiv · 2411.12012

Liouville theorems for harmonic 1-forms on gradient Ricci solitons

Chenghong He·Di Wu·Xi Zhang
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Abstract

We prove that there is no nontrivial $L^2$-integrable harmonic 1-form on noncompact complete gradient steady Ricci solitons or noncompact complete gradient shrinking K\"{a}hler-Ricci solitons. As an application, it can be used to distinguish certain flat vector bundles that arise from fundamental group representations into $SL(r,\mathbb{C})$.

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Chenghong He, Di Wu, Xi Zhang. 2024-11-18. Liouville theorems for harmonic 1-forms on gradient Ricci solitons. https://arxiv.org/abs/2411.12012

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