The hyperbolic rank of homogeneous Hadamard manifolds
type: Item
instance of: scholarly article
title: The hyperbolic rank of homogeneous Hadamard manifolds
zbMATH Open document ID: 1020.53017
author: Thomas Foertsch
published in: Manuscripta Mathematica
publication date: 2002-12-01T00:00:00Z
review text: Let \(H\) denote a homogeneous Hadamard manifold. For information on such manifolds we refer to [\textit{T. H. Wolter}, Geometry of homogeneous Hadamard manifolds, Int. J. Math. 2, 223-234 (1991; Zbl 0722.53046)]. Consider all geodesic hyperbolic spaces \(Y\) quasi-isometrically embedded into \(H\). In this paper, the author proves that \(\text{rank}_E(H)+\text{rank}_{\text{hyp}}(H)\geq\dim(H)\). It is important to mention that the above result was first proved by N. Brady and B. Farb, in 1998, for a Riemannian product space, followed by E. Leuzinger, in 2000, for symmetric spaces of non-compact type.
reviewed by: Krishan Lal Duggal
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 1837305
zbMATH Keywords: Hadamard manifold
zbMATH Keywords: homogeneous spaces
zbMATH Keywords: rank
zbMATH Keywords: geodesic hyperbolic spaces
MaRDI profile type: Publication
full work available at URL: s00229-002-0294-8
OpenAlex ID: W2041358491
DOI: 10.1007/S00229-002-0294-8
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description: scientific article; zbMATH DE number 1837305