Classification of closed conformally flat Lorentzian manifolds with unipotent holonomy
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916245787377664 |
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| author | Lee, Rachel Melnick, Karin |
| author_facet | Lee, Rachel Melnick, Karin |
| contents | We classify closed, conformally flat Lorentzian manifolds of dimension $n \geq 3$ with unipotent holonomy in PO(2,n). They are all Kleinian and fall into four different geometric types according to the intersection of the image of the developing map with a holonomy-invariant isotropic flag. They are homeomorphic to $S^{n-1} \times S^1$ or a nilmanifold of degree at most three, up to a finite cover. We classify those admitting an essential conformal flow; these fall into two geometric types, both homeomorphic to $S^{n-1} \times S^1$ up to finite cover. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_08410 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of closed conformally flat Lorentzian manifolds with unipotent holonomy Lee, Rachel Melnick, Karin Differential Geometry Geometric Topology 53C50, 57N16 We classify closed, conformally flat Lorentzian manifolds of dimension $n \geq 3$ with unipotent holonomy in PO(2,n). They are all Kleinian and fall into four different geometric types according to the intersection of the image of the developing map with a holonomy-invariant isotropic flag. They are homeomorphic to $S^{n-1} \times S^1$ or a nilmanifold of degree at most three, up to a finite cover. We classify those admitting an essential conformal flow; these fall into two geometric types, both homeomorphic to $S^{n-1} \times S^1$ up to finite cover. |
| title | Classification of closed conformally flat Lorentzian manifolds with unipotent holonomy |
| topic | Differential Geometry Geometric Topology 53C50, 57N16 |
| url | https://arxiv.org/abs/2405.08410 |