Infinitesimal Conformal Rigidity on Damek-Ricci Spaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908824190844928 |
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| author | Satoh, Hiroyasu Shah, Hemangi Madhusudan |
| author_facet | Satoh, Hiroyasu Shah, Hemangi Madhusudan |
| contents | We show that every conformal vector field on a Damek-Ricci space is necessarily Killing, establishing a strong form of infinitesimal conformal rigidity. Although this rigidity phenomenon is classically known in the Einstein setting, our proof follows a completely different approach. We formulate the conformal Killing condition as an explicit system of partial differential equations on the solvable Lie group model and analyze it directly. This local and analytic method yields a constructive proof of rigidity without relying on global arguments or transformation groups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_18137 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinitesimal Conformal Rigidity on Damek-Ricci Spaces Satoh, Hiroyasu Shah, Hemangi Madhusudan Differential Geometry 53C24, 53C25, 53C35 We show that every conformal vector field on a Damek-Ricci space is necessarily Killing, establishing a strong form of infinitesimal conformal rigidity. Although this rigidity phenomenon is classically known in the Einstein setting, our proof follows a completely different approach. We formulate the conformal Killing condition as an explicit system of partial differential equations on the solvable Lie group model and analyze it directly. This local and analytic method yields a constructive proof of rigidity without relying on global arguments or transformation groups. |
| title | Infinitesimal Conformal Rigidity on Damek-Ricci Spaces |
| topic | Differential Geometry 53C24, 53C25, 53C35 |
| url | https://arxiv.org/abs/2507.18137 |