Isometry groups of three-dimensional Lie groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866915183374368768 |
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| author | Cosgaya, Ana Reggiani, Silvio |
| author_facet | Cosgaya, Ana Reggiani, Silvio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_08924 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Isometry groups of three-dimensional Lie groups Cosgaya, Ana Reggiani, Silvio Differential Geometry 53C30, 53C35 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. |
| title | Isometry groups of three-dimensional Lie groups |
| topic | Differential Geometry 53C30, 53C35 |
| url | https://arxiv.org/abs/2105.08924 |