A nonintegrable sub-Riemannian geodesic flow on a Carnot group
Artikel i vetenskaplig tidskrift, 1997

Graded nilpotent Lie groups, or Carnot groups, are to sub-Riemannian geometry as Euclidean spaces are to Riemannian geometry. They are the metric tangent cones for this geometry. Hoping that the analogy between sub-Riemannian and Riemannian geometry is a strong one, one might conjecture that the sub-Riemannian geodesic flow on any Carnot group is completely integrable. We prove this conjecture to be false by showing that the sub-Riemannian geodesic flow is not algebraically completely integrable in the case of the group whose Lie algebra consists of 4 by 4 upper triangular matrices. As a corollary, we prove that the centralizer for the corresponding quadratic "quantum" Hamiltonian in the universal enveloping algebra of this Lie algebra is "as small as possible."

Universal enveloping algebra

Carnot groups

Sub-Riemannian

Nonholonomic distributions

Nonintegrable

Författare

R. Montgomery

M. Shapiro

Alexander Stolin

Institutionen för matematik

Göteborgs universitet

Journal of Dynamical and Control Systems

1079-2724 (ISSN)

Vol. 3 4 519-530

Ämneskategorier

Matematik