Global Stability of Special Multi-Flags

In this paper, we study special multi-flags on manifolds. A special multiflag is a certain nested sequence of subbundles of the tangent bundle which are derived by Lie brackets. A property of a special multi-flag is characterized by the existence of a completely integrable subdistribution of corank one in the largest distribution in the sequence, which is a so-called covariant subdistribution. It is proved that a one-parameter deformation of a special multi-flag on a compact manifold can be described by a family of global diffeomorphisms of the underlying manifold, if the covariant subdistribution of the largest distribution in the flag is preserved.