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Sub-Riemannian structures on 3D lie groups

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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 consequence, we explicitly find a sub-Riemannian isometry between the nonisomorphic Lie groups SL(2) and A +(\( \mathbb{R} \)) × S 1, where A +(\( \mathbb{R} \)) denotes the group of orientation preserving affine maps on the real line.

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Authors and Affiliations

  1. SISSA, Trieste, Italy

    A. Agrachev & D. Barilari

  2. Steklov Mathematical Institute, Moscow, Russia

    A. Agrachev

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  1. A. Agrachev
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  2. D. Barilari
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Correspondence to A. Agrachev.

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Agrachev, A., Barilari, D. Sub-Riemannian structures on 3D lie groups. J Dyn Control Syst 18, 21–44 (2012). https://doi.org/10.1007/s10883-012-9133-8

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  • DOI: https://doi.org/10.1007/s10883-012-9133-8

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