Xavier, Frederico A non-immersion theorem for hyperbolic manifolds. (English) Zbl 0566.53045 Comment. Math. Helv. 60, 280-283 (1985). 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 \({\mathbb{R}}^{2n-1}\). Reviewer: H.Reckziegel Cited in 2 ReviewsCited in 7 Documents MSC: 53C40 Global submanifolds 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) Keywords:hyperbolic space; isometry group; hyperbolic manifold PDFBibTeX XMLCite \textit{F. Xavier}, Comment. Math. Helv. 60, 280--283 (1985; Zbl 0566.53045) Full Text: DOI EuDML