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Isometric Embeddings of Asymptotically Hyperbolic Manifolds into Hyperbolic Space
Abstract
The Nash Embedding theorem asserts that every closed Riemannian manifold can be isometrically embedded into a Euclidean space of sufficiently high dimension. In this paper, we address the asymptotically hyperbolic version of the problem. We prove that an asymptotically hyperbolic manifold (M,g) can be realized as a submanifold of a sufficiently high-dimensional hyperbolic space HN+1, intersecting the sphere at infinity transversely, if and only if g is asymptotically Poincaré-Einstein to second order.
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BibTeX
@misc{usula2026isometric,
title = {{Isometric Embeddings of Asymptotically Hyperbolic Manifolds into Hyperbolic Space}},
author = {Marco Usula},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40962},
eprint = {2610.40962},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40962},
}
RIS
TY - UNPB
TI - Isometric Embeddings of Asymptotically Hyperbolic Manifolds into Hyperbolic Space
AU - Marco Usula
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40962
UR - https://arxiv.org/abs/2610.40962
AB - The Nash Embedding theorem asserts that every closed Riemannian manifold can be isometrically embedded into a Euclidean space of sufficiently high dimension. In this paper, we address the asymptotically hyperbolic version of the problem. We prove that an asymptotically hyperbolic manifold (M,g) can be realized as a submanifold of a sufficiently high-dimensional hyperbolic space H^N+1, intersecting the sphere at infinity transversely, if and only if g is asymptotically Poincaré-Einstein to second order.
ER -