%0 Journal Article %J Journal of Dynamical and Control Systems. Volume 18, Issue 1, January 2012, Pages 21-44 %D 2012 %T Sub-Riemannian structures on 3D Lie groups %A Andrei A. Agrachev %A Davide Barilari %X

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.

%B Journal of Dynamical and Control Systems. Volume 18, Issue 1, January 2012, Pages 21-44 %I SISSA %G en %U http://hdl.handle.net/1963/6453 %1 6397 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-02-05T13:48:29Z\r\nNo. of bitstreams: 1\r\n1007.4970v2.pdf: 453953 bytes, checksum: 4330325299743bad4afe9f1ac7121e21 (MD5) %R 10.1007/s10883-012-9133-8