A.A. Agrachev, D. Barilari, Sub-Riemanian structures on 3D Lie groups

Title: Sub-Riemanian structures on 3D Lie groups
Authors: A.A. Agrachev, D. Barilari
Journal title: Dynamical and Control Systems
Year: 2012
Volume: 18
Pages: 21-44

We give a complete classification of left-invariant sub-Riemannian structures on three dimensional Lie groups in terms of the basic differential invariants. As a corollary we explicitly find a sub-Riemannian isometry between the nonisomorphic Lie groups SL(2) and A^+ (R) × S^1, where A^+ (R) denotes the group of orientation preserving affine maps on the real line.

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