GEOMETRIC APPROACH TO GOURSAT FLAGS * Richard ...

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Lemma 2.2. Let (F) be the Goursat ag generated byadistribution D = D sanddescribed bythe tuple ! 1 :::! s of 1-forms. Dene the 2-forms i (p) by (2.1). Then forany point p of the manifold and for any i =1 2:::s we have:rank i (p) =2L(D i )(p) =ker i (p):Example. Let D be the corank s Goursat distribution described by the 1-forms (C).Then the tuple (! 1 :::! s ) describes the ag (F) generated by D = D s , and the foliationL(D i )isdescribed by the 1-forms dx dy dz 1 :::dz i .Proof of lemmata 2.1 and 2.2. We rstshowthat the rank of i (p) istwo, fori
Page 1 and 2: GEOMETRIC APPROACH TO GOURSAT FLAGS
Page 4 and 5: Theorem 1. Apply the Cartan prolong
Page 8 and 9: these two hyperplanes will be diere
Page 10 and 11: The fact that d!j V 6=0implies that
Page 13 and 14: if and only if E(p) and ~ E(p) belo
Page 16 and 17: The orbits A-E can be easily descri
Page 18 and 19: transformation is realized for at l
Page 20 and 21: is a submersion. In this case we wi
Page 22 and 23: prolonging, beginning with a surfac
Page 24 and 25: Proof of Proposition 6.1. The proof
Page 26 and 27: By the sandwich lemma L(D s;1 )(p)
Page 28 and 29: X t of vector elds on M. The relati
Page 30 and 31: R1. Let 2 Symm p (D). Then we can
Page 32 and 33: set I = f3 4g f3 4:::7g, one can re
Page 34 and 35: Proof of Proposition D1. We showtha
Page 36: 1995 Gershkovich V., Exotic Engel S

GEOMETRIC APPROACH TO GOURSAT FLAGS * Richard ...

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