A construction of metrics of negative Ricci curvature
type: Item
instance of: scholarly article
title: A construction of metrics of negative Ricci curvature
zbMATH Open document ID: 0628.53043
author: Robert Brooks
published in: Journal of Differential Geometry
publication date: 1989-01-01T00:00:00Z
review text: This paper gives a construction of metrics of negative Ricci curvature on all compact 3-manifolds. The existence of such a metric was previously demonstrated by Gao and Yau. The construction given here relies on the existence of tubular neighborhoods of specified width about short geodesics in hyperbolic 3-manifolds, and also makes use of the Hilden- Lozano-Montesinos theory of universal knots. It is shown that there are positive constants a and b such that every 3-manifold carries a metric whose Ricci curvatures are pinched between -a and -b. A generalization to some manifolds of higher dimension is also given.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 4022086
zbMATH Keywords: negative Ricci curvature
zbMATH Keywords: compact 3-manifolds
zbMATH Keywords: hyperbolic 3-manifolds
zbMATH Keywords: universal knots
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214442634
OpenAlex ID: W1516178572
Wikidata QID: Q115182956
DOI: 10.4310/JDG/1214442634
description: scientific article; zbMATH DE number 4022086