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 +(ℝ)×S 1, where A +(ℝ) denotes the group of orientation preserving affine maps on the real line. © 2012 Springer Science+Business Media, LLC.

Sub-Riemannian structures on 3D lie groups

Agrachev A.;Barilari D.
2012

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 consequence, we explicitly find a sub-Riemannian isometry between the nonisomorphic Lie groups SL(2) and A +(ℝ)×S 1, where A +(ℝ) denotes the group of orientation preserving affine maps on the real line. © 2012 Springer Science+Business Media, LLC.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3401932
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 62
  • ???jsp.display-item.citation.isi??? 59
social impact