@Article{IJNAM-13-5,
author = {Léonard-Fortuné, D. and Miara, B. and Vallée, C.},
title = {Equivalence Between Riemann-Christoffel and Gauss-Codazzi-Mainardi Conditions for a Shell},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2016},
volume = {13},
number = {5},
pages = {820--830},
abstract = {<p style="text-align: justify;">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&#39;s moving frames.</p>},
issn = {2617-8710},
doi = {https://doi.org/2016-IJNAM-467},
url = {https://global-sci.com/article/83266/equivalence-between-riemann-christoffel-and-gauss-codazzi-mainardi-conditions-for-a-shell}
}