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Sub-Riemannian structures on 3D Lie groups

TitleSub-Riemannian structures on 3D Lie groups
Publication TypeJournal Article
Year of Publication2012
AuthorsAgrachev, AA, Barilari, D
JournalJournal of Dynamical and Control Systems. Volume 18, Issue 1, January 2012, 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 $A^+(\mathbb{R})\times S^1$, where $A^+(\mathbb{R})$ denotes the group of orientation preserving affine maps on the real line.


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