A codimension 3 sub-Riemannian structure on the Gromoll-Meyer exotic sphere

We construct a codimension 3 completely non-holonomic subbundle on the Gromoll-Meyer exotic 7-sphere based on its realization as a base space of a Sp(2)-principal bundle with the structure group Sp(1). The same method can be applied to construct a codimension 3 completely non-holonomic subbundle on the standard 7-sphere (or more general on a (4n+3)-dimensional standard sphere). In the latter case such a construction based on the Hopf bundle is well-known. Our method provides a new and simple proof for the standard sphere S7.