Displaying similar documents to “The Group of Isometries of a Left Invariant Riemannian Metric on a Lie Group.”

On naturally reductive left-invariant metrics of SL ( 2 , ℝ )

Stefan Halverscheid, Andrea Iannuzzi (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On any real semisimple Lie group we consider a one-parameter family of left-invariant naturally reductive metrics. Their geodesic flow in terms of Killing curves, the Levi Civita connection and the main curvature properties are explicitly computed. Furthermore we present a group theoretical revisitation of a classical realization of all simply connected 3-dimensional manifolds with a transitive group of isometries due to L. Bianchi and É. Cartan. As a consequence one obtains a characterization...

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

Rory Biggs (2017)

Communications in Mathematics

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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...