Characteristic vector fields of generic distributions of corank 2

  • B. Jakubczyk

    Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warsaw 10, Poland
  • W. Kryński

    Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warsaw 10, Poland
  • F. Pelletier

    LAMA, Université de Savoie, Campus Scientifique, 73376 Le Bourget du Lac, France

Abstract

We study generic distributions of corank 2 on manifolds of dimension . We describe singular curves of such distributions, also called abnormal curves. For even the singular directions (tangent to singular curves) are discrete lines in , while for odd they form a Veronese curve in a projectivized subspace of , at generic . We show that singular curves of a generic distribution determine the distribution on the subset of where they generate at least two different directions. In particular, this happens on the whole of if 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 is even.

Cite this article

B. Jakubczyk, W. Kryński, F. Pelletier, Characteristic vector fields of generic distributions of corank 2. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 1, pp. 23–38

DOI 10.1016/J.ANIHPC.2007.05.006