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

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.
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Agrachev, Andrey; Barilari, D.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/13907
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