Surfaces with extreme value curvature in Alexandrov spaces
type: Item
instance of: scholarly article
title: Surfaces with extreme value curvature in Alexandrov spaces
zbMATH Open document ID: 0847.53023
author: Chang-Wan Kim
author: Jin-Whan Yim
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1996-02-26T00:00:00Z
review text: An Alexandrov space \(X\) is a locally compact complete length space with curvature bounded either below or above in the distance comparison sense. Consider \(M_1\) be an exponential image of a plane, \(M_2\) be a ruled surface produced by a parallel line field along a geodesic. Then \(\text{curv}_p (X) = k\) \((k\) the bound of the curvature) for \(p \in M_i\), \(i = 1,2\), if and only if \(M_i\) is totally geodesic in \(X\) and locally isometric to the 2-space form of curvature \(k\).
reviewed by: Valentin Boju
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C45
Mathematics Subject Classification ID: 53C70
zbMATH DE Number: 847735
zbMATH Keywords: exponential map
zbMATH Keywords: constant curvature
zbMATH Keywords: Alexandrov space
zbMATH Keywords: ruled surface
zbMATH Keywords: parallel line field
zbMATH Keywords: locally isometric
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178225455
OpenAlex ID: W2017034521
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DOI: 10.2748/TMJ/1178225455
description: scientific article; zbMATH DE number 847735