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arXiv · 2105.08924

Isometry groups of three-dimensional Lie groups

Ana Cosgaya·Silvio Reggiani
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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.

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Ana Cosgaya, Silvio Reggiani. 2021-05-19. Isometry groups of three-dimensional Lie groups. https://doi.org/10.1007/s10455-022-09835-3

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