A non-immersion theorem for hyperbolic manifolds
type: Item
instance of: scholarly article
title: A non-immersion theorem for hyperbolic manifolds
zbMATH Open document ID: 0566.53045
DOI: 10.1007/BF02567414
author: Frederico Xavier
published in: Commentarii Mathematici Helvetici
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/140013
review text: It has been conjectured for a long time that the hyperbolic space \({\mathbb{H}}^ n\) cannot be isometrically immersed into \({\mathbb{R}}^{2n-1}\). The author represents a partial verification: If \(\Gamma\) is a discrete subgroup of the isometry group of \({\mathbb{H}}^ n\), whose limit set in the sphere at infinity has more than two elements, then the hyperbolic manifold \({\mathbb{H}}^ n/\Gamma\) cannot be isometrically immersed into \({\mathbb{R}}^{2n-1}\).
reviewed by: Helmut Reckziegel
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 3903501
zbMATH Keywords: hyperbolic space
zbMATH Keywords: isometry group
zbMATH Keywords: hyperbolic manifold
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3903501