Geodesic
Isometries of Riemannian and sub-Riemannian structures on three-dimensional Lie groups
Communications in Mathematics, Tome 25 (2017) no. 2, pp. 99-135.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We investigate the isometry groups of the left-invariant Riemannian and sub-Riemannian structures on simply connected three-dimensional Lie groups. More specifically, we determine the isometry group for each normalized structure and hence characterize for exactly which structures (and groups) the isotropy subgroup of the identity is contained in the group of automorphisms of the Lie group. It turns out (in both the Riemannian and sub-Riemannian cases) that for most structures any isometry is the composition of a left translation and a Lie group automorphism.
Classification : 22E30, 53C17, 53C20
Keywords: Riemannian structures; sub-Riemannian structures; three-dimensional Lie groups 
@article{COMIM_2017__25_2_a2,
     author = {Biggs, Rory},
     title = {Isometries of {Riemannian} and {sub-Riemannian} structures on three-dimensional {Lie} groups},
     journal = {Communications in Mathematics},
     pages = {99--135},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {2017},
     mrnumber = {3745432},
     zbl = {1395.53034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2017__25_2_a2/}
}
TY  - JOUR
AU  - Biggs, Rory
TI  - Isometries of Riemannian and sub-Riemannian structures on three-dimensional Lie groups
JO  - Communications in Mathematics
PY  - 2017
SP  - 99
EP  - 135
VL  - 25
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/COMIM_2017__25_2_a2/
LA  - en
ID  - COMIM_2017__25_2_a2
ER  - 
%0 Journal Article
%A Biggs, Rory
%T Isometries of Riemannian and sub-Riemannian structures on three-dimensional Lie groups
%J Communications in Mathematics
%D 2017
%P 99-135
%V 25
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/COMIM_2017__25_2_a2/
%G en
%F COMIM_2017__25_2_a2
Biggs, Rory. Isometries of Riemannian and sub-Riemannian structures on three-dimensional Lie groups. Communications in Mathematics, Tome 25 (2017) no. 2, pp. 99-135. http://geodesic.mathdoc.fr/item/COMIM_2017__25_2_a2/