$C^{1}$-isometric embeddings of Riemannian spaces in Lorentzian spaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912445347397632 |
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| author | Boukholkhal, Alaa |
| author_facet | Boukholkhal, Alaa |
| contents | 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 $F: (V,g) \rightarrow (W,h)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19333 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $C^{1}$-isometric embeddings of Riemannian spaces in Lorentzian spaces Boukholkhal, Alaa Differential Geometry 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 $F: (V,g) \rightarrow (W,h)$. |
| title | $C^{1}$-isometric embeddings of Riemannian spaces in Lorentzian spaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2407.19333 |