The hyperbolic nspace as a graph in Euclidean (6n−6)space
Nettekoven, Wolfgang and Henke, Wolfgang
(1987)
The hyperbolic nspace as a graph in Euclidean (6n−6)space.
Published in:
Manuscripta mathematica Vol. 59 (1).
pp. 1320.
Abstract
Let Hsp n denote the ndimensional hyperbolic space of constant curvature (1) and Esp N the Ndimensional Euclidean space. {it D. Blanusa} [Monatsh. Math. 59, 217229 (1955; Zbl. 67, 144)] constructed an isometric Csp{infty}imbedding Hsp 2 o Esp 6 whose image is the graph of a Csp{infty}map {bfR}sp 2 o {bfR}sp 4. For nge 3, in the same article, Blanusa was only able to construct a 11 isometric Csp{infty}immersion Hsp n o Esp{6n5} which is not an imbedding in the strong sense (i.e. not a homeomorphism onto a topological subspace). The present paper generalizes the stronger 2 dimensional result of Blanusa. Theorem: For each nge 2, there exists an isometric Csp{infty}imbedding Hsp n o Esp{6n6} whose image is the graph of a Cmap {bfR}sp n o {bfR}sp{5n6}. Moreover explicit formulas are given which apply to the isometric imbedding problem for a larger class of Riemannian manifolds.
Item Type:  Article 

Citations:  No citation data. 
Uncontrolled Keywords:  Euclidean space graphs hyperbolic space isometric imbedding 
Subjects: 

Divisions:  Mathematical Institute 
Related URLs: 
ZAIK Number:  zpr86037 

Depositing User:  Archive Admin 
Date Deposited:  02 Apr 2001 00:00 
Last Modified:  19 Jan 2012 12:36 
URI:  http://earchive.informatik.unikoeln.de/id/eprint/37 