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

cm:9468 - Communications in Mathematics, January 11, 2018, Volume 25 (2017), Issue 2 - https://doi.org/10.1515/cm-2017-0010
Isometries of Riemannian and sub-Riemannian structures on three-dimensional Lie groupsArticle

Authors: Rory Biggs ORCID

    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.

    https://doi.org/10.1515/cm-2017-0010
    Source: HAL:hal-03664942v1
    Volume: Volume 25 (2017), Issue 2
    Published on: January 11, 2018
    Imported on: May 11, 2022
    Keywords: General Mathematics,[MATH]Mathematics [math]
    Licence: Attribution-Non Commercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
    Funding:
      Source : OpenAIRE Graph
    • Lie groups, differential equations and geometry; Funder: European Commission; Code: 317721

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