Intrinsic complements of equiregular sub-Riemannian manifolds
  Under a nondegeneracy condition, we show that an equiregular sub-Riemannian manifold of step size $r$ admits a canonical, $V$-rigid complement defined from the sub-Riemannian data that is preserved the by action of sub-Riemannian isometries. We explore how the existence of such a complement relates to results from the literature and study the step size 2 case in more detail. 
Robert K. Hladky
math.DG