SO$(2,n)$-compatible embeddings of conformally flat $n$-dimensional submanifolds in $\mathbb{R}^{n+2}$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866911800065261568 |
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| author | Huguet, E. Queva, J. Renaud, J. |
| author_facet | Huguet, E. Queva, J. Renaud, J. |
| contents | We describe embeddings of $n$-dimensional Lorentzian manifolds, including Friedmann-Lemaître-Robertson-Walker spaces, in $\mathbb{R}^{n+2}$ such that the metrics of the submanifolds are inherited by a restriction from that of $\mathbb{R}^{n+2}$, and the action of the linear group SO$(2, n)$ of the ambient space reduces to conformal transformations on the submanifolds. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_05049 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | SO$(2,n)$-compatible embeddings of conformally flat $n$-dimensional submanifolds in $\mathbb{R}^{n+2}$ Huguet, E. Queva, J. Renaud, J. Mathematical Physics General Relativity and Quantum Cosmology Differential Geometry 53B25 We describe embeddings of $n$-dimensional Lorentzian manifolds, including Friedmann-Lemaître-Robertson-Walker spaces, in $\mathbb{R}^{n+2}$ such that the metrics of the submanifolds are inherited by a restriction from that of $\mathbb{R}^{n+2}$, and the action of the linear group SO$(2, n)$ of the ambient space reduces to conformal transformations on the submanifolds. |
| title | SO$(2,n)$-compatible embeddings of conformally flat $n$-dimensional submanifolds in $\mathbb{R}^{n+2}$ |
| topic | Mathematical Physics General Relativity and Quantum Cosmology Differential Geometry 53B25 |
| url | https://arxiv.org/abs/2312.05049 |