We give a complete classication 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)xS^1, where A^+(R) denotes the group of orientation preserving affine transformations of the real line.
Sub-Riemanian structures on 3D Lie groups
Agrachev, Andrey;
2012-01-01
Abstract
We give a complete classication 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)xS^1, where A^+(R) denotes the group of orientation preserving affine transformations of the real line.File in questo prodotto:
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