Liouville theorems for harmonic 1-forms on gradient Ricci solitons
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915083231166464 |
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| author | He, Chenghong Wu, Di Zhang, Xi |
| author_facet | He, Chenghong Wu, Di Zhang, Xi |
| contents | 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 Kähler-Ricci solitons. As an application, it can be used to distinguish certain flat vector bundles that arise from fundamental group representations into $SL(r,\mathbb{C})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12012 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Liouville theorems for harmonic 1-forms on gradient Ricci solitons He, Chenghong Wu, Di Zhang, Xi Differential Geometry Complex Variables 35B53, 53C25 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 Kähler-Ricci solitons. As an application, it can be used to distinguish certain flat vector bundles that arise from fundamental group representations into $SL(r,\mathbb{C})$. |
| title | Liouville theorems for harmonic 1-forms on gradient Ricci solitons |
| topic | Differential Geometry Complex Variables 35B53, 53C25 |
| url | https://arxiv.org/abs/2411.12012 |