SubRiemannian geodesics for Carnot groups of step 3
  In Carnot groups of step 3, all subriemannian geodesics are proved to be normal. The proof is based on a reduction argument and the Goh condition for minimality of singular curves. The Goh condition is deduced from a reformulation and a calculus of the end-point mapping which boils down to the graded structures of Carnot groups. 
Kanghai Tan and Xiaoping Yang
math.DG