Warped products of Hadamard spaces
type: Item
instance of: scholarly article
title: Warped products of Hadamard spaces
zbMATH Open document ID: 0909.53050
author: Richard L. Bishop
author: Stephanie B. Alexander
published in: Manuscripta Mathematica
publication date: 1999-04-08T00:00:00Z
review text: Geodesics in a warped product \(B\times_fF\) of intrinsic metric spaces are examined. Since the projection of a geodesic to the base \(B\) is essentially independent of the fibre, conservative mechanics makes sense in any intrinsic metric space. Let \(B\) and \(F\) be Hadamard spaces. The main result here states that \(B\times_fF\) is a Hadamard space for any positive convex function \(f\) on \(B\). The same statement holds for the class of complete metric spaces of curvature at most \(0\) in the sense of Alexandrov.
Mathematics Subject Classification ID: 53C70
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 1208705
zbMATH Keywords: geodesics
zbMATH Keywords: warped product
zbMATH Keywords: intrinsic metric spaces
reviewed by: Cornelia-Livia Bejan
MaRDI profile type: Publication
full work available at URL: s002290050078
OpenAlex ID: W2086711256
DOI: 10.1007/S002290050078
description: scientific article; zbMATH DE number 1208705