Isometric Embeddings of Conformally Compact Manifolds into Hyperbolic Spaces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912753584701440 |
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| author | Usula, Marco |
| author_facet | Usula, Marco |
| contents | The celebrated Nash Embedding Theorem asserts that every closed Riemannian manifold can be isometrically embedded into a sufficiently high-dimensional Euclidean space. In this paper, we prove an analogous result in the conformally compact context. Let $\left(M,g\right)$ be a conformally compact manifold whose sectional curvature at infinity is strictly bounded below by a negative constant $-λ^{2}$. We prove that $\left(M,g\right)$ can be realized as a submanifold, transverse to the sphere at infinity, of a sufficiently high-dimensional rescaled hyperbolic space of constant curvature $-λ^{2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07231 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isometric Embeddings of Conformally Compact Manifolds into Hyperbolic Spaces Usula, Marco Differential Geometry 53-XX The celebrated Nash Embedding Theorem asserts that every closed Riemannian manifold can be isometrically embedded into a sufficiently high-dimensional Euclidean space. In this paper, we prove an analogous result in the conformally compact context. Let $\left(M,g\right)$ be a conformally compact manifold whose sectional curvature at infinity is strictly bounded below by a negative constant $-λ^{2}$. We prove that $\left(M,g\right)$ can be realized as a submanifold, transverse to the sphere at infinity, of a sufficiently high-dimensional rescaled hyperbolic space of constant curvature $-λ^{2}$. |
| title | Isometric Embeddings of Conformally Compact Manifolds into Hyperbolic Spaces |
| topic | Differential Geometry 53-XX |
| url | https://arxiv.org/abs/2512.07231 |