Let Ω be a simply-connected open subset of . We show in this Note that, if a smooth enough field U of symmetric and positive-definite matrices of order three satisfies the compatibility relation (due to C. Vallée)
. Soit Ω un ouvert simplement connexe de . On montre dans cette Note que, si un champ suffisamment régulier U de matrices symétriques définies positives d'ordre trois satisfait la relation de compatibilité (due à C. Vallée)
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Philippe G. Ciarlet 1; Liliana Gratie 2; Oana Iosifescu 3; Cristinel Mardare 4; Claude Vallée 5
@article{CRMATH_2006__343_6_415_0, author = {Philippe G. Ciarlet and Liliana Gratie and Oana Iosifescu and Cristinel Mardare and Claude Vall\'ee}, title = {Rotation fields and the fundamental theorem of {Riemannian} geometry in $ {\mathbb{R}}^{3}$}, journal = {Comptes Rendus. Math\'ematique}, pages = {415--421}, publisher = {Elsevier}, volume = {343}, number = {6}, year = {2006}, doi = {10.1016/j.crma.2006.08.007}, language = {en}, }
TY - JOUR AU - Philippe G. Ciarlet AU - Liliana Gratie AU - Oana Iosifescu AU - Cristinel Mardare AU - Claude Vallée TI - Rotation fields and the fundamental theorem of Riemannian geometry in $ {\mathbb{R}}^{3}$ JO - Comptes Rendus. Mathématique PY - 2006 SP - 415 EP - 421 VL - 343 IS - 6 PB - Elsevier DO - 10.1016/j.crma.2006.08.007 LA - en ID - CRMATH_2006__343_6_415_0 ER -
%0 Journal Article %A Philippe G. Ciarlet %A Liliana Gratie %A Oana Iosifescu %A Cristinel Mardare %A Claude Vallée %T Rotation fields and the fundamental theorem of Riemannian geometry in $ {\mathbb{R}}^{3}$ %J Comptes Rendus. Mathématique %D 2006 %P 415-421 %V 343 %N 6 %I Elsevier %R 10.1016/j.crma.2006.08.007 %G en %F CRMATH_2006__343_6_415_0
Philippe G. Ciarlet; Liliana Gratie; Oana Iosifescu; Cristinel Mardare; Claude Vallée. Rotation fields and the fundamental theorem of Riemannian geometry in $ {\mathbb{R}}^{3}$. Comptes Rendus. Mathématique, Volume 343 (2006) no. 6, pp. 415-421. doi : 10.1016/j.crma.2006.08.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.08.007/
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