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arXiv · 1401.6026

On Isometric Embeddings into Anti-de Sitter Space-times

Ye-Kai Wang·Chen-Yun Lin
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Abstract

We show that any metric on $S^2$ with Gauss curvature $K \geq -κ$ admits a $C^{1,1}$-isometric embedding into the hyperbolic space with sectional curvature $-κ$. We also give a sufficient condition for a metric on $S^2$ to be isometrically embedded into anti-de Sitter spacetime with the prescribed cosmological time function.

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Ye-Kai Wang, Chen-Yun Lin. 2014-01-23. On Isometric Embeddings into Anti-de Sitter Space-times. https://arxiv.org/abs/1401.6026

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