×

A non-immersion theorem for hyperbolic manifolds. (English) Zbl 0566.53045

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

MSC:

53C40 Global submanifolds
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
PDFBibTeX XMLCite
Full Text: DOI EuDML