The integral of the scalar curvature of complete manifolds without conjugate points
type: Item
instance of: scholarly article
title: The integral of the scalar curvature of complete manifolds without conjugate points
zbMATH Open document ID: 0761.53021
author: Florêncio F. Guimarães
published in: Journal of Differential Geometry
publication date: 1993-04-01T00:00:00Z
review text: The main result of the paper states that, on a complete Riemannian manifold \(M\) without conjugate points and integrable (on the unit tangent bundle) positive or negative part of the Ricci curvature, the integral of the scalar curvature is non-positive and, unless \(M\) is flat, strictly negative. This generalises results of E. Hopf, Green and others.
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 146367
zbMATH Keywords: complete manifolds without conjugate points
zbMATH Keywords: Ricci curvature
zbMATH Keywords: scalar curvature
reviewed by: Werner Ballmann
Wikidata QID: Q115180414
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214453184
OpenAlex ID: W1562468438
DOI: 10.4310/JDG/1214453184
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description: scientific article; zbMATH DE number 146367