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arXiv · 2407.19333

$C^{1}$-isometric embeddings of Riemannian spaces in Lorentzian spaces

Alaa Boukholkhal
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Abstract

For any compact Riemannian manifold $(V,g)$ and any Lorentzian manifold $(W,h)$, we prove that any spacelike embedding $f: V \rightarrow W$ that is long ($g\leq f^{*}h$) can be $C^{0}$-approximated by a $C^{1}$ isometric embedding $F: (V,g) \rightarrow (W,h)$.

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Alaa Boukholkhal. 2024-07-27. $C^{1}$-isometric embeddings of Riemannian spaces in Lorentzian spaces. https://arxiv.org/abs/2407.19333

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