Differential Geometry
A canonical frame for nonholonomic rank two distributions of maximal class
Comptes Rendus. Mathématique, Volume 342 (2006) no. 8, pp. 589-594.

In 1910 E. Cartan constructed the canonical frame and found the most symmetric case for maximally nonholonomic rank 2 distributions in R5. We solve the analogous problems for rank 2 distributions in Rn for arbitrary n>5. Our method is a kind of symplectification of the problem and it is completely different from the Cartan method of equivalence.

En 1910 E. Cartan a construit un repère canonique et a trouvé le cas le plus symétrique des distributions de rang 2 et non holonômes de manière maximale dans R5. Nous résolvons ici des problèmes analogues pour les distributions de rang 2 dans Rn avec n>5 arbitraire. Notre méthode est une sorte de symplectification du problème et est complètement différente de la méthode par équivalence de Cartan.

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DOI: 10.1016/j.crma.2006.02.010
Doubrov, Boris 1; Zelenko, Igor 2

1 The Faculty of Applied Mathematics, Belorussian State University, F. Skaryny Ave. 4, Minsk, Belarus 220050, Belarus
2 SISSA, via Beirut 2–4, 34014 Trieste, Italy
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Doubrov, Boris; Zelenko, Igor. A canonical frame for nonholonomic rank two distributions of maximal class. Comptes Rendus. Mathématique, Volume 342 (2006) no. 8, pp. 589-594. doi : 10.1016/j.crma.2006.02.010. http://www.numdam.org/articles/10.1016/j.crma.2006.02.010/

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