English

Submanifolds of Constant Negative Curvature: A Generalization of Hilbert's Theorem

Differential Geometry 2025-12-02 v1

Abstract

We use the generalized Gauss-Bonnet formula for Riemannian polyhedra discovered by Allendoerfer, Weil and Chern to show that hyperbolic space of dimension nn has no isometric immersion into Euclidean space of dimension 2n12n-1.

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Cite

@article{arxiv.2512.00973,
  title  = {Submanifolds of Constant Negative Curvature: A Generalization of Hilbert's Theorem},
  author = {John Douglas Moore},
  journal= {arXiv preprint arXiv:2512.00973},
  year   = {2025}
}

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46 pages