Extension of a Riemannian metric with vanishing curvature.
type: Item
instance of: scholarly article
title: Extension of a Riemannian metric with vanishing curvature.
zbMATH Open document ID: 1066.53080
author: Philippe G. Ciarlet
author: Cristinel Mardare
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2004-03-15T00:00:00Z
review text: The authors prove the following theorem: Let \(\Omega\) be a simply-connected open subset of \(\mathbb R^n\) satisfying the strong geodesic property and let be given a Riemannian metric \((g_{ij})\) of class \(\mathcal{C}^2\) and of vanishing curvature in \(\Omega\), such that the functions \(g_{ij}\) and their partial derivatives of order \(\leqslant 2\) have continuous extensions to \(\overline\Omega\). Then there exists a connected open subset \(\widetilde\Omega\) of \(\mathbb R^n\) containing \(\overline\Omega\) and a Riemannian metric \((\tilde g_{ij})\) of class \(\mathcal{C}^2\) and of vanishing curvature in \(\widetilde\Omega\) that extends the metric \((g_{ij})\).
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 2057120
zbMATH Keywords: Riemannian metric
zbMATH Keywords: Riemann curvature tensor
zbMATH Keywords: extension of a metric
reviewed by: Marian Hotloś
MaRDI profile type: Publication
full work available at URL: j.crma.2003.12.017
OpenAlex ID: W2051449612
Wikidata QID: Q115358333
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DOI: 10.1016/J.CRMA.2003.12.017
description: scientific article; zbMATH DE number 2057120