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 has no isometric immersion into Euclidean space of dimension .
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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