TY - JOUR T1 - Sub-Riemannian structures on 3D Lie groups JF - Journal of Dynamical and Control Systems. Volume 18, Issue 1, January 2012, Pages 21-44 Y1 - 2012 A1 - Andrei A. Agrachev A1 - Davide Barilari AB -

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 $A^+(\mathbb{R})\times S^1$, where $A^+(\mathbb{R})$ denotes the group of orientation preserving affine maps on the real line.

PB - SISSA UR - http://hdl.handle.net/1963/6453 U1 - 6397 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER -