Sectional curvature and the determination of the metric in space-time
type: Item
instance of: scholarly article
title: Sectional curvature and the determination of the metric in space-time
zbMATH Open document ID: 0535.53023
DOI: 10.1007/BF00764019
published in: General Relativity and Gravitation
publication date: 1984-01-01T00:00:00Z
review text: The known result that the curvature tensor of a Lorentz manifold determines the metric (in almost all cases) uniquely, remains true, if one takes the sectional curvature instead. Theorem: If two Lorentzian metrics g and g' on M have the same sectional curvatures for all (non null) tangent two spaces, g and g' are conformally related to any region of non constant curvature and are equal to any subregion which is not conformally flat.
Mathematics Subject Classification ID: 53B30
zbMATH DE Number: 3850015
zbMATH Keywords: sectional curvature
zbMATH Keywords: Lorentzian metrics
author: G. S. Hall
MaRDI profile type: Publication
Wikidata QID: Q125382599
cites work: Curvature collineations and the determination of the metric from the curvature in General Relativity
cites work: On regular curvature structures
cites work: The partially ordered set of all J-classes of a finite semigroup
cites work: Curvature and the Petrov Canonical Forms
cites work: Riemannian curvature and the classification of the Riemann and Ricci tensors in space-time
cites work: Curvature and metric
cites work: The Large Scale Structure of Space-Time
cites work: Invariant Formulation of Gravitational Radiation Theory
cites work: The classification of the Ricci tensor in general relativity theory
cites work: On Ruse's Spaces of Recurrent Curvature
cites work: Recurrence conditions in space-time
cites work: Q4049364
full work available at URL: https://doi.org/10.1007/bf00764019
OpenAlex ID: W2095296972
description: scientific article; zbMATH DE number 3850015