dc.contributor.author |
Biggs, Rory
|
|
dc.date.accessioned |
2018-02-08T05:26:19Z |
|
dc.date.available |
2018-02-08T05:26:19Z |
|
dc.date.issued |
2017 |
|
dc.description.abstract |
We investigate the isometry groups of the left-invariant Rieman-
nian and sub-Riemannian structures on simply connected three-dimensional
Lie groups. More speci cally, we determine the isometry group for each nor-
malized 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. |
en_ZA |
dc.description.department |
Mathematics and Applied Mathematics |
en_ZA |
dc.description.librarian |
am2018 |
en_ZA |
dc.description.sponsorship |
The research leading to these results has received funding from the European
Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement
no. 317721. The author was primarily funded by the Claude Leon Foundation
during the course of this research. |
en_ZA |
dc.description.uri |
https://www.degruyter.com/view/j/cm |
en_ZA |
dc.identifier.citation |
Biggs, R. 2017, 'Isometries of Riemannian and sub-Riemannian structures on three-dimensional Lie groups', Communications in Mathematics, vol. 25, no. 2, pp. 99-135. |
en_ZA |
dc.identifier.issn |
2336-1298 (online) |
|
dc.identifier.other |
10.1515/cm-2017-0010 |
|
dc.identifier.uri |
http://hdl.handle.net/2263/63887 |
|
dc.language.iso |
en |
en_ZA |
dc.publisher |
De Gruyter Open |
en_ZA |
dc.rights |
© 2017 The University of Ostrava |
en_ZA |
dc.subject |
Riemannian structures |
en_ZA |
dc.subject |
Sub-Riemannian structures |
en_ZA |
dc.subject |
Three-dimensional Lie groups |
en_ZA |
dc.title |
Isometries of Riemannian and sub-Riemannian structures on three-dimensional Lie groups |
en_ZA |
dc.type |
Article |
en_ZA |