Homogeneous structures of $3$-dimensional Lie groups
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912194563670016 |
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| author | Inoguchi, Jun-ichi Ohno, Yu |
| author_facet | Inoguchi, Jun-ichi Ohno, Yu |
| contents | We give a classification of homogeneous Riemannian structures on (non locally symmetric) $3$-dimensional Lie groups equipped with left invariant Riemannian metrics. This work together with classifications due to previous works yields a complete classification of all the homogeneous Riemannian structures on homogeneous Riemannian $3$-spaces. Two applications of the classification to contact Riemannian geometry and CR geometry are also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homogeneous structures of $3$-dimensional Lie groups Inoguchi, Jun-ichi Ohno, Yu Differential Geometry We give a classification of homogeneous Riemannian structures on (non locally symmetric) $3$-dimensional Lie groups equipped with left invariant Riemannian metrics. This work together with classifications due to previous works yields a complete classification of all the homogeneous Riemannian structures on homogeneous Riemannian $3$-spaces. Two applications of the classification to contact Riemannian geometry and CR geometry are also given. |
| title | Homogeneous structures of $3$-dimensional Lie groups |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2501.11321 |