Submanifolds of Constant Negative Curvature: A Generalization of Hilbert's Theorem
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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.