Unique isometric immersion into hyperbolic space
type: Item
instance of: scholarly article
title: Unique isometric immersion into hyperbolic space
zbMATH Open document ID: 0784.53032
DOI: 10.1155/S0161171293000900
author: M. C. Fu
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1994-04-06T00:00:00Z
full work available at URL: https://eudml.org/doc/46924
review text: The main result of the paper establishes sufficient conditions under which two isometric immersions \(f_ 1\), \(f_ 2\) of a connected, orientable Riemannian \(n\)-manifold into the \((n+1)\)-hyperbolic space \(H^{n+1}\) are equivalent up to an isometry \(\tau\) of \(H^{n+1}\), i.e., \(\tau f_ 2=f_ 1\). As in the classical corresponding case of isometric immersions into the \((n+1)\)-Euclidean space, the result is formulated in terms of the Gauss maps of \(f_ 1\) and \(f_ 2\). The author's approach relies on the general rigidity study for hypersurfaces in \(H^{n+1}\).
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 438925
zbMATH Keywords: Gauss maps
zbMATH Keywords: rigidity
reviewed by: Dumitru Motreanu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 438925