A Classification of Sub-Riemannian Structures on the Heisenberg Groups

作者：Biggs Rory^*; Nagy Peter T

来源：Acta Polytechnica Hungarica, 2013, 10(7): 41-52.

• Heisenberg group
• sub-Riemannian geometry
• isometry
• symplectic group
• invariant optimal control
• cost-equivalence

We apply Williamson's theorem for the diagonalization of quadratic forms by symplectic matrices to sub-Riemannian (and Riemannian) structures on the Heisenberg groups. A classification of these manifolds, under isometric Lie group automorphisms, is obtained. A (parametrized) list of equivalence class representatives is identified; a geometric characterization of this equivalence relation is provided. A corresponding classification of (drift-free) invariant optimal control problems is exhibited.

• 出版日期2013