Nearly geodesic immersions and domains of discontinuity
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866908493602095104 |
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| author | Davalo, Colin |
| author_facet | Davalo, Colin |
| contents | We study nearly geodesic immersions in higher rank symmetric spaces of non-compact type, which we define as immersions that satisfy a bound on their fundamental form, generalizing the notion of immersions in hyperbolic space with principal curvature in $(-1,1)$. This notion depends on the choice of a flag manifold embedded in the visual boundary, and immersions satisfying this bound admit a natural domain in this flag manifold that comes with a fibration. As an application we give an explicit fibration of some domains of discontinuity for some Anosov representations. Our method can be applied in particular to some $Θ$-positive representations for each notion of $Θ$-positivity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11260 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nearly geodesic immersions and domains of discontinuity Davalo, Colin Differential Geometry Geometric Topology 53C35 (Primary) 22E40 (Secondary) We study nearly geodesic immersions in higher rank symmetric spaces of non-compact type, which we define as immersions that satisfy a bound on their fundamental form, generalizing the notion of immersions in hyperbolic space with principal curvature in $(-1,1)$. This notion depends on the choice of a flag manifold embedded in the visual boundary, and immersions satisfying this bound admit a natural domain in this flag manifold that comes with a fibration. As an application we give an explicit fibration of some domains of discontinuity for some Anosov representations. Our method can be applied in particular to some $Θ$-positive representations for each notion of $Θ$-positivity. |
| title | Nearly geodesic immersions and domains of discontinuity |
| topic | Differential Geometry Geometric Topology 53C35 (Primary) 22E40 (Secondary) |
| url | https://arxiv.org/abs/2303.11260 |