Flat sub-Riemannian structures are local approximations — nilpotentizations — of sub-Riemannian structures at regular points. Lie algebras of symmetries of flat maximal growth distributions and sub-Riemannian structures of rank two are computed in dimensions 3, 4, and 5.
Title: Symmetries of flat rank two distributions and sub-Riemannian Structures
Authors: Yu. L. Sachkov
Journal title: Transactions of the American Mathematical Society