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.
2012
18
1
21
44
Agrachev, Andrey; Barilari, D.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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/20.500.11767/13907
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 69
  • ???jsp.display-item.citation.isi??? 64
social impact