Sub-Riemannian (2, 3, 5, 6)-Structures

Abstract We describe all Carnot algebras with growth vector (2, 3, 5, 6), their normal forms, an invariant that separates them, and a change of basis transforms such algebra into form. For each form, Casimir functions symplectic foliations on the Lie coalgebra are computed. An forms left-invariant 6)-distributions described. A classification, up to isometries, sub-Riemannian structures 6)-Carnot groups is obtained.