| Title | Sub-Riemannian structures on 3D Lie groups |
| Publication Type | Journal Article |
| Year of Publication | 2012 |
| Authors | Agrachev, AA, Barilari, D |
| Journal | Journal of Dynamical and Control Systems. Volume 18, Issue 1, January 2012, Pages 21-44 |
| Abstract | 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. |
| URL | http://hdl.handle.net/1963/6453 |
| DOI | 10.1007/s10883-012-9133-8 |