Inserted: 19 jul 2013
Last Updated: 17 nov 2020
Journal: Comm. Anal. and Geom.
We introduce a family of extremal polynomial associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterization of abnormal subriemannian geodesics in stratified nilpotent Lie groups. They satisfy a set of remarkable structure relations that are used to integrate the adjoint equations.
Keywords: Carnot groups, SubRiemannian geometry, Abnormal extremals, Extremal polynomials