Year: 2016
Author: D. Léonard-Fortuné, B. Miara, C. Vallée
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 5 : pp. 820–830
Abstract
We establish the equivalence between the vanishing three-dimensional Riemann- Christoffel curvature tensor of a shell and the two-dimensional Gauss-Codazzi-Mainardi compatibility conditions on its middle surface. Additionally, we produce a new proof of Gauss theorema egregium and Bonnet theorem (reconstructing a surface from its two fundamental forms). This is performed in the very elegant framework of Cartan's moving frames.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-IJNAM-467
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 5 : pp. 820–830
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Surfaces 3D manifolds Pfaffian systems Frobenius integrability conditions Riemann-Christoffel curvature tensor moving frames Cartan differential geometry Tensorial calculus.