Proper Almost-Homogeneous Domains of the Einstein Universe
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909702832521216 |
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| author | Chalumeau, Adam Galiay, Blandine |
| author_facet | Chalumeau, Adam Galiay, Blandine |
| contents | The Einstein universe $\mathbf{Ein}^{p,q}$ of signature $(p,q)$ is a pseudo-Riemannian analogue of the conformal sphere; it is the conformal compactification of the pseudo-Riemannian Minkowski space. For $p,q \geq 1$, we show that, up to a conformal transformation, there is only one almost-homogeneous domain in $\mathbf{Ein}^{p,q}$ that is bounded in a suitable stereographic projection. This domain, which we call a diamond, is a model for the symmetric space of $\operatorname{PO}(p,1) \times \operatorname{PO}(1,q)$. We deduce a classification of closed conformally flat manifolds with proper development. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18577 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Proper Almost-Homogeneous Domains of the Einstein Universe Chalumeau, Adam Galiay, Blandine Differential Geometry Group Theory Geometric Topology Metric Geometry The Einstein universe $\mathbf{Ein}^{p,q}$ of signature $(p,q)$ is a pseudo-Riemannian analogue of the conformal sphere; it is the conformal compactification of the pseudo-Riemannian Minkowski space. For $p,q \geq 1$, we show that, up to a conformal transformation, there is only one almost-homogeneous domain in $\mathbf{Ein}^{p,q}$ that is bounded in a suitable stereographic projection. This domain, which we call a diamond, is a model for the symmetric space of $\operatorname{PO}(p,1) \times \operatorname{PO}(1,q)$. We deduce a classification of closed conformally flat manifolds with proper development. |
| title | Proper Almost-Homogeneous Domains of the Einstein Universe |
| topic | Differential Geometry Group Theory Geometric Topology Metric Geometry |
| url | https://arxiv.org/abs/2407.18577 |