Failure of Lichnerowicz-type result in parabolic geometries of real rank at least $3$
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909993859547136 |
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| author | Aldape, Toby |
| author_facet | Aldape, Toby |
| contents | Given a Yamaguchi nonrigid parabolic model geometry $(G,P)$ with $G$ simple of real rank at least $3$, we use techniques developed by Erickson to establish the existence of closed, nonflat, essential, regular, normal Cartan geometries modeled on $(G,P)$. Yamaguchi nonrigidity is a necessary condition for admitting nonflat, regular, normal examples. This rules out Lichnerowicz-type conjectures for these model geometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12542 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Failure of Lichnerowicz-type result in parabolic geometries of real rank at least $3$ Aldape, Toby Differential Geometry Given a Yamaguchi nonrigid parabolic model geometry $(G,P)$ with $G$ simple of real rank at least $3$, we use techniques developed by Erickson to establish the existence of closed, nonflat, essential, regular, normal Cartan geometries modeled on $(G,P)$. Yamaguchi nonrigidity is a necessary condition for admitting nonflat, regular, normal examples. This rules out Lichnerowicz-type conjectures for these model geometries. |
| title | Failure of Lichnerowicz-type result in parabolic geometries of real rank at least $3$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2509.12542 |