TY - JOUR
T1 - Equivalence Between Riemann-Christoffel and Gauss-Codazzi-Mainardi Conditions for a Shell
AU - Léonard-Fortuné , D.
AU - Miara , B.
AU - Vallée , C.
JO - International Journal of Numerical Analysis and Modeling
VL - 5
SP - 820
EP - 830
PY - 2016
DA - 2016/09
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/467.html
KW - Surfaces, 3D manifolds, Pfaffian systems, Frobenius integrability conditions, Riemann-Christoffel curvature tensor, moving frames, Cartan differential geometry, Tensorial calculus.
AB - <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>