Examples of manifolds of positive Ricci curvature
type: Item
instance of: scholarly article
title: Examples of manifolds of positive Ricci curvature
zbMATH Open document ID: 0633.53064
author: Ji-Ping Sha
author: Da-Gang Yang
published in: Journal of Differential Geometry
publication date: 1989-01-01T00:00:00Z
review text: This paper presents some new examples of simply connected Riemannian manifolds with positive Ricci curvature, which admit no metric with nonnegative sectional curvature, in both compact and noncompact cases. Specifically, these examples show that there is not an upper bound on the total Betti number for manifolds with positive Ricci curvature in a fixed dimension, and a manifold with positive Ricci curvature can be of infinite topological type if it is non-compact. They thus settle a long standing problem in Riemannian geometry.
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 4030437
zbMATH Keywords: positive Ricci curvature
zbMATH Keywords: non-negative sectional curvature
zbMATH Keywords: total Betti number
zbMATH Keywords: infinite topological type
Wikidata QID: Q115182931
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214442635
OpenAlex ID: W1513515668
DOI: 10.4310/JDG/1214442635
description: scientific article; zbMATH DE number 4030437