Pinching constants for hyperbolic manifolds
type: Item
instance of: scholarly article
title: Pinching constants for hyperbolic manifolds
zbMATH Open document ID: 0646.53037
DOI: 10.1007/BF01404671
author: William P. Thurston
author: Misha Gromov
published in: Inventiones Mathematicae
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143471
review text: This paper exhibits very interesting examples of n-manifolds M, \(n\geq 4\), with negative sectional curvature, \(K_ M\). On the one hand, for every \(k<-1\) there is a closed negatively curved manifold M, which carries no metric satisfying \(k\leq K_ M\leq -1\). On the other hand for any \(k<-1\) there is a closed manifold M with \(k\leq K_ m\leq -1\) which does not carry a metric with constant negative curvature. This latter statement is in sharp contrast to the situation for positively curved manifolds [cf. the reviewer, \textit{H. Karcher} and \textit{E. A. Ruh}, Invent. Math. 23, 31- 48 (1974; Zbl 0271.53044); Math. Ann. 211, 7-21 (1974; Zbl 0273.53051)].
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 4054503
zbMATH Keywords: pinching theorems
zbMATH Keywords: examples
zbMATH Keywords: negative sectional curvature
zbMATH Keywords: constant negative curvature
Wikidata QID: Q56483329
reviewed by: Karsten Grove
MaRDI profile type: Publication
cites work: Manifolds of negative curvature
cites work: Filling Riemannian manifolds
cites work: Group actions and curvature
cites work: The Gromov invariant of negatively curved manifolds
cites work: A compact Kähler surface of negative curvature not covered by the ball
description: scientific article; zbMATH DE number 4054503