We find relative differential invariants of orders eight and nine for a planar nonparallelizable 3-web such that their vanishing is necessary and sufficient for a 3-web to be linearizable. This solves the Blaschke conjecture for 3-webs.
Nous présentons des invariants relatifs différentiels d'ordre huit et neuf pour un 3-tissu plan non parallélisable dont l'annulation est nécessaire et suffisante pour que la 3-tissu soit linéarisable. Ceci apporte une solution a la conjecture de Blaschke pour le problème de linéarisation des 3-tissus.
Accepted:
Published online:
Vladislav V. Goldberg 1; Valentin V. Lychagin 2
@article{CRMATH_2005__341_3_169_0, author = {Vladislav V. Goldberg and Valentin V. Lychagin}, title = {On linearization of planar three-webs and {Blaschke's} conjecture}, journal = {Comptes Rendus. Math\'ematique}, pages = {169--173}, publisher = {Elsevier}, volume = {341}, number = {3}, year = {2005}, doi = {10.1016/j.crma.2005.06.017}, language = {en}, }
Vladislav V. Goldberg; Valentin V. Lychagin. On linearization of planar three-webs and Blaschke's conjecture. Comptes Rendus. Mathématique, Volume 341 (2005) no. 3, pp. 169-173. doi : 10.1016/j.crma.2005.06.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.06.017/
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