Left-invariant Sub-Riemannian Engel structures: abnormal geodesics and   integrability
  We provide the first known family of examples of integrable homogeneous sub-Riemannian structures admitting strictly abnormal geodesics. These examples were obtained through the analysis of the equivalence problem for sub-Riemannian Engel structures. We formulate a criterion of strict abnormality in terms of structure functions of a canonical frame on a sub-Riemannian Engel manifold as well as estimates on conjugate times. 
Ivan Beschastnyi and Alexandr Medvedev
math.DG math.OC