Totally Geodesic Submanifolds in Products of Non-Positively Curved Manifolds
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917379958636544 |
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| author | Hanson, Nicholas |
| author_facet | Hanson, Nicholas |
| contents | We study non-positively curved closed manifolds $M$ and $n$-dimensional totally geodesic submanifolds of $M \times M$ which satisfy a transversality condition. We prove that, under some mild irreducibility requirements on $M$, if $M \times M$ admits infinitely many such submanifolds or just a single dense such submanifold, then $M$ is a locally symmetric space. In proving this, we prove a stronger version which only requires such submanifolds to exist in the universal cover $\widetilde M \times \widetilde M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01415 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Totally Geodesic Submanifolds in Products of Non-Positively Curved Manifolds Hanson, Nicholas Differential Geometry Geometric Topology 53A35 We study non-positively curved closed manifolds $M$ and $n$-dimensional totally geodesic submanifolds of $M \times M$ which satisfy a transversality condition. We prove that, under some mild irreducibility requirements on $M$, if $M \times M$ admits infinitely many such submanifolds or just a single dense such submanifold, then $M$ is a locally symmetric space. In proving this, we prove a stronger version which only requires such submanifolds to exist in the universal cover $\widetilde M \times \widetilde M$. |
| title | Totally Geodesic Submanifolds in Products of Non-Positively Curved Manifolds |
| topic | Differential Geometry Geometric Topology 53A35 |
| url | https://arxiv.org/abs/2604.01415 |