Cartan Flat Non-degenerate CR Lie Groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910010647248896 |
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| author | Hasegawa, Keizo Kasuya, Hisashi |
| author_facet | Hasegawa, Keizo Kasuya, Hisashi |
| contents | In this paper we determine all the simply connected non-degenerate CR Lie groups, which are flat with respect to the Cartan connection: in terms of associated Lie algebras, we assert that the only Cartan flat non-degenerate CR Lie algebras are $\mathfrak{su}(2)$, $\mathfrak{sl}(2,\mathbb{R})$, $\mathfrak{aff}(\mathbb{R}) \oplus \mathbb{R}$, and $\mathfrak{h}_{2m+1}$ with its modifications, where $\mathfrak{aff}(\mathbb{R})$ is the affine Lie algebra of dimension 2 and $\mathfrak{h}_{2m+1}$ is the Heisenberg Lie algebra of dimension $2m+1$. Furthermore, we determine all the (flat and non-flat) non-degenerate CR structures on each of these Lie groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03318 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cartan Flat Non-degenerate CR Lie Groups Hasegawa, Keizo Kasuya, Hisashi Differential Geometry 51M15, 53D35, 32V05 In this paper we determine all the simply connected non-degenerate CR Lie groups, which are flat with respect to the Cartan connection: in terms of associated Lie algebras, we assert that the only Cartan flat non-degenerate CR Lie algebras are $\mathfrak{su}(2)$, $\mathfrak{sl}(2,\mathbb{R})$, $\mathfrak{aff}(\mathbb{R}) \oplus \mathbb{R}$, and $\mathfrak{h}_{2m+1}$ with its modifications, where $\mathfrak{aff}(\mathbb{R})$ is the affine Lie algebra of dimension 2 and $\mathfrak{h}_{2m+1}$ is the Heisenberg Lie algebra of dimension $2m+1$. Furthermore, we determine all the (flat and non-flat) non-degenerate CR structures on each of these Lie groups. |
| title | Cartan Flat Non-degenerate CR Lie Groups |
| topic | Differential Geometry 51M15, 53D35, 32V05 |
| url | https://arxiv.org/abs/2404.03318 |