Weyl metrizability of 3-dimensional projective structures and CR submanifolds
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908841688432640 |
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| author | Makhmali, Omid |
| author_facet | Makhmali, Omid |
| contents | A projective structure is Weyl metrizable if it has a representative that preserves a conformal structure. We interpret Weyl metrizability of 3-dimensional projective structures as certain 5-dimensional nondegenerate CR submanifolds in a class of 7-dimensional 2-nondegenerate CR structures. As a corollary, it follows that in dimension three Beltrami's theorem extends to conformal structures, i.e. a locally flat projective structure is Weyl metrizable exclusively with respect to a locally flat conformal structure. In higher dimensions it is shown that conformal Beltrami theorem remains true as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07460 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weyl metrizability of 3-dimensional projective structures and CR submanifolds Makhmali, Omid Differential Geometry Primary: 53A20, 53C18, 32V05, 53C28, 53A55, 32V40, 53C05, Secondary: 53C24 A projective structure is Weyl metrizable if it has a representative that preserves a conformal structure. We interpret Weyl metrizability of 3-dimensional projective structures as certain 5-dimensional nondegenerate CR submanifolds in a class of 7-dimensional 2-nondegenerate CR structures. As a corollary, it follows that in dimension three Beltrami's theorem extends to conformal structures, i.e. a locally flat projective structure is Weyl metrizable exclusively with respect to a locally flat conformal structure. In higher dimensions it is shown that conformal Beltrami theorem remains true as well. |
| title | Weyl metrizability of 3-dimensional projective structures and CR submanifolds |
| topic | Differential Geometry Primary: 53A20, 53C18, 32V05, 53C28, 53A55, 32V40, 53C05, Secondary: 53C24 |
| url | https://arxiv.org/abs/2501.07460 |