On uniqueness of submaximally symmetric parabolic geometries
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866909074268880896 |
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| author | The, Dennis |
| author_facet | The, Dennis |
| contents | Among (regular, normal) parabolic geometries of type $(G,P)$, there is a locally unique maximally symmetric structure and it has symmetry dimension $\dim(G)$. The symmetry gap problem concerns the determination of the next realizable (submaximal) symmetry dimension. When $G$ is a complex or split-real simple Lie group of rank at least three or when $(G,P) = (G_2,P_2)$, we establish a local uniqueness result for submaximally symmetric structures of type $(G,P)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_10500 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On uniqueness of submaximally symmetric parabolic geometries The, Dennis Differential Geometry Primary 58J70, Secondary 53B99, 22E46, 17B70 Among (regular, normal) parabolic geometries of type $(G,P)$, there is a locally unique maximally symmetric structure and it has symmetry dimension $\dim(G)$. The symmetry gap problem concerns the determination of the next realizable (submaximal) symmetry dimension. When $G$ is a complex or split-real simple Lie group of rank at least three or when $(G,P) = (G_2,P_2)$, we establish a local uniqueness result for submaximally symmetric structures of type $(G,P)$. |
| title | On uniqueness of submaximally symmetric parabolic geometries |
| topic | Differential Geometry Primary 58J70, Secondary 53B99, 22E46, 17B70 |
| url | https://arxiv.org/abs/2107.10500 |