Isometries of Riemannian and sub-Riemannian structures on three-dimensional Lie groups

Rory Biggs

Communications in Mathematics (2017)

  • Volume: 25, Issue: 2, page 99-135
  • ISSN: 1804-1388

Abstract

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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.

How to cite

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Biggs, Rory. "Isometries of Riemannian and sub-Riemannian structures on three-dimensional Lie groups." Communications in Mathematics 25.2 (2017): 99-135. <http://eudml.org/doc/294613>.

@article{Biggs2017,
abstract = {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.},
author = {Biggs, Rory},
journal = {Communications in Mathematics},
keywords = {Riemannian structures; sub-Riemannian structures; three-dimensional Lie groups},
language = {eng},
number = {2},
pages = {99-135},
publisher = {University of Ostrava},
title = {Isometries of Riemannian and sub-Riemannian structures on three-dimensional Lie groups},
url = {http://eudml.org/doc/294613},
volume = {25},
year = {2017},
}

TY - JOUR
AU - Biggs, Rory
TI - Isometries of Riemannian and sub-Riemannian structures on three-dimensional Lie groups
JO - Communications in Mathematics
PY - 2017
PB - University of Ostrava
VL - 25
IS - 2
SP - 99
EP - 135
AB - 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.
LA - eng
KW - Riemannian structures; sub-Riemannian structures; three-dimensional Lie groups
UR - http://eudml.org/doc/294613
ER -

References

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