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

2025/11/30 by Moore, John Douglas
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.00973

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.

Citations

• Isometric immersions with flat normal bundle between space forms
• Isometric immersions with flat normal bundle between space forms
• On the complexity of isometric immersions of hyperbolic spaces in any\n codimension

Related

• Hilbert's Theorem, via moving frames
• On the complexity of isometric immersions of hyperbolic spaces in any\n codimension
• A new obstruction to minimal isometric immersions into a real space form
• Isometric Immersion of Complete Surfaces with Slowly Decaying Negative Gauss Curvature
• Convexity, Rigidity, and Reduction of Codimension of Isometric Immersions into Space Forms