Characteristic vector fields of generic distributions of corank 2

We study generic distributions D subset of TM of corank 2 on manifolds M of dimension n >= 5. We describe singular curves of such distributions, also called abnormal curves. For it even the Singular directions (tangent to singular Curves) are discrete lines in D(x), while for it odd they form a Veronese curve in a projectivized subspace of D(x). at generic X E M, We show that singular curves of a generic distribution determine file distribution on the Subset of M where they generate at least two different directions. In particular, this happens on the whole of M if it is odd. The distribution is determined by characteristic vector fields and their Lie brackets of appropriate order. We characterize pairs of vector fields which can appear as characteristic vector fields of a generic corank 2 distribution, when it is even. (c) 2007 Elsevier Masson SAS. All rights reserved.