Isometry groups of three-dimensional Lie groups

Abstract

We compute the full isometry group of any left invariant metric on a simply connected, non-unimodular Lie group of dimension three. As an application, we determine the index of symmetry of such metrics and prove that the singularities of the moduli space of left-invariant metrics, up to isometric automorphism, is contained in the subspace of classes of metrics with maximal index of symmetry.

14 pages, 2 tables

References in corpus (1)

• The index of symmetry for a left-invariant metric on a solvable three-dimensional Lie group

Cited by in corpus (2)

• Isometries of 3-dimensional semi-Riemannian Lie groups
• Polar actions on homogeneous 3-spaces