On the recovery of a surface with prescribed first and second fundamental forms.
type: Item
instance of: scholarly article
title: On the recovery of a surface with prescribed first and second fundamental forms.
zbMATH Open document ID: 1044.53004
DOI: 10.1016/S0021-7824(01)01236-3
author: Philippe G. Ciarlet
author: François Larsonneur
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2003-09-25T00:00:00Z
review text: The paper proves Bonnet's theorem as a corollary of the known theorem which states that if the Riemann-Christoffel tensor associated with a field of positive definite symmetric matrices of order three vanishes in a connected and simply connected open set in \(\mathbb{R}^3\), then this field is the metric tensor field of an open set that can be isometrically imbedded in \(\mathbb{R}^3\) uniquely up to rigid motions.
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 1985990
zbMATH Keywords: Bonnet's theorem
zbMATH Keywords: Riemann-Christoffel tensor
zbMATH Keywords: field of positive definite symmetric matrices
reviewed by: Ivan C. Sterling
MaRDI profile type: Publication
cites work: Compatibility conditions for a left Cauchy-Green strain field
cites work: Q4091004
cites work: Q4165939
cites work: Q4039741
cites work: Q4485429
cites work: Sur la détermination d'une surface dans à partir de ses deux formes fondamentales
cites work: Q3664012
cites work: Q5683877
cites work: Q4768281
cites work: A dynamical theory of structures solids. I Basic developments
cites work: On isometric immersions of Riemannian manifolds in euclidean space
cites work: On isometric immersions of riemannian manifolds
full work available at URL: s0021-7824(01)01236-3
OpenAlex ID: W2054082083
description: scientific article; zbMATH DE number 1985990