On the Inoue-Bombieri construction
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918237251305472 |
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| author | Flamencourt, Brice Zeghib, Abdelghani |
| author_facet | Flamencourt, Brice Zeghib, Abdelghani |
| contents | We study compact quotients of a Riemannian product $\mathbb{R}^q \times (N, g_N)$, where $(N, g_N)$ is a complete Riemannian manifold, by discrete subgroups $Γ$ of $\mathrm{Sim}(\mathbb{R}^q) \times \mathrm{Isom}(N)$. When $N$ is a symmetric space of non-compact type, this construction generalizes the well-known Inoue--Bombieri surfaces. We show that this setting is actually equivalent to that of the so-called LCP manifolds, and we establish a Bieberbach-type rigidity result in the case where $N$ is symmetric. In addition, we provide a classification of the manifolds $N$ and the groups $Γ$ when $N$ is a Hadamard manifold with strictly negative curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03389 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Inoue-Bombieri construction Flamencourt, Brice Zeghib, Abdelghani Differential Geometry We study compact quotients of a Riemannian product $\mathbb{R}^q \times (N, g_N)$, where $(N, g_N)$ is a complete Riemannian manifold, by discrete subgroups $Γ$ of $\mathrm{Sim}(\mathbb{R}^q) \times \mathrm{Isom}(N)$. When $N$ is a symmetric space of non-compact type, this construction generalizes the well-known Inoue--Bombieri surfaces. We show that this setting is actually equivalent to that of the so-called LCP manifolds, and we establish a Bieberbach-type rigidity result in the case where $N$ is symmetric. In addition, we provide a classification of the manifolds $N$ and the groups $Γ$ when $N$ is a Hadamard manifold with strictly negative curvature. |
| title | On the Inoue-Bombieri construction |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2505.03389 |