Another approach to the fundamental theorem of Riemannian geometry in \(\mathbb R^{3}\), by way of rotation fields

DOI10.1016/j.matpur.2006.10.009zbMath1114.53033OpenAlexW2159257039WikidataQ115343606 ScholiaQ115343606MaRDI QIDQ877008

Liliana Gratie, Oana Iosifescu, Philippe G. Ciarlet, Claude Vallee, Christinel Mardare

Publication date: 19 April 2007

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2006.10.009

zbMATH Keywords

Pfaff systemspolar factorizationclassical differential geometryfundamental theorem of Riemannian geometrynonlinear three-dimensional elasticity

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20)

Related Items (8)

Integrability conditions between the first and second Cosserat deformation tensor in geometrically nonlinear micropolar models and existence of minimizers ⋮ New compatibility conditions for the fundamental theorem of surface theory ⋮ Rotation fields and the fundamental theorem of Riemannian geometry in \(\mathbb R^3\) ⋮ On the determination of deformation from strain ⋮ A new approach to the fundamental theorem of surface theory ⋮ Justification of the Darboux-Vallée-Fortuné compatibility relation in the theory of surfaces ⋮ A new approach to the fundamental theorem of surface theory, by means of the Darboux-Vallée-Fortuné compatibility relation ⋮ Compatibility conditions of continua using Riemann–Cartan geometry

Cites Work

• Unnamed Item
• Unnamed Item
• The fundamental theorem of surface theory for surfaces with little regularity
• Rotation fields and the fundamental theorem of Riemannian geometry in \(\mathbb R^3\)
• A new look at the compatibility problem of elasticity theory
• Finite rotations in the description of continuum deformation
• On the rotated stress tensor and the material version of the Doyle- Ericksen formula
• Compatibility equations for large deformations
• On the recovery of a surface with prescribed first and second fundamental forms.
• Existence of a solution for an unsteady elasticity problem in large displacement and small perturbation
• Recovery of a manifold with boundary and its continuity as a function of its metric tensor
• An introduction to continuum mechanics
• A new variational principle for finite elastic displacements
• RECOVERY OF A SURFACE WITH BOUNDARY AND ITS CONTINUITY AS A FUNCTION OF ITS TWO FUNDAMENTAL FORMS
• Interprétation géométrique de la décomposition des équations de compatibilité en grandes déformations
• The Rotation Associated with Large Strains
• ON THE RECOVERY OF A MANIFOLD WITH PRESCRIBED METRIC TENSOR
• ON ISOMETRIC IMMERSIONS OF A RIEMANNIAN SPACE WITH LITTLE REGULARITY

This page was built for publication: Another approach to the fundamental theorem of Riemannian geometry in \(\mathbb R^{3}\), by way of rotation fields