  Consider a manifold, of dimension greater than 3, equipped with a
bracket-generating distribution. In this article we prove complete h-principles
for embedded regular horizontal curves and for embedded transverse curves.
These results contrast with the 3-dimensional contact case, where the full
h-principle for transverse/legendrian knots is known not to hold.
  We also prove analogous statements for immersions, with no assumptions on the
ambient dimension.

Differential Geometry