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 $2n-1$.

46 pages