Collapsing Riemannian manifolds to the circle
type: Item
instance of: scholarly article
title: Collapsing Riemannian manifolds to the circle
zbMATH Open document ID: 0661.53029
DOI: 10.1007/BF01215261
author: Xiao-Wei Peng
published in: Mathematische Zeitschrift
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174092
review text: In this paper we study the manifolds which collapse to a circle. The main result is to prove that if the Riemannian manifold collapses to a circle, then the manifold admits a finite covering space which is homeomorphic to a compact solv-manifold for the dimension \(n\neq 4\).
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 4080315
zbMATH Keywords: collapse to a circle
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: covering space
zbMATH Keywords: solv-manifold
Wikidata QID: Q115393862
MaRDI profile type: Publication
cites work: Q3909666
cites work: Collapsing Riemannian manifolds while keeping their curvature bounded. I
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cites work: Almost flat manifolds
cites work: Q5624419
cites work: Discrete subgroups of solvable Lie groups. I
OpenAlex ID: W371214913
description: scientific article; zbMATH DE number 4080315