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arXiv · 2312.05049

SO$(2,n)$-compatible embeddings of conformally flat $n$-dimensional submanifolds in $\mathbb{R}^{n+2}$

E. Huguet·J. Queva·J. Renaud
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Abstract

We describe embeddings of $n$-dimensional Lorentzian manifolds, including Friedmann-Lema\^itre-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.

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BibTeXRIS

E. Huguet, J. Queva, J. Renaud. 2023-12-08. SO$(2,n)$-compatible embeddings of conformally flat $n$-dimensional submanifolds in $\mathbb{R}^{n+2}$. https://doi.org/10.1103/physrevd.109.064054

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