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

John Douglas Moore

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arXiv · 2512.00973

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

John Douglas Moore

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Abstract

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

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John Douglas Moore. 2025-11-30. Submanifolds of Constant Negative Curvature: A Generalization of Hilbert's Theorem. https://arxiv.org/abs/2512.00973

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