A non-immersion theorem for hyperbolic manifolds (Q1059291)

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 \({\mathbb{R}}^{2n-1}\).