Geodesic loops and orthogonal geodesic chords without self-intersections
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911104444137472 |
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| author | Rademacher, Hans-Bert |
| author_facet | Rademacher, Hans-Bert |
| contents | We show that for a generic Riemannian metric on a compact manifold of dimension $n\ge 3$ all geodesic loops based at a fixed point have no self-intersections. We also show that for an open and dense subset of the space of Riemannian metrics on an $n$-disc with $n \ge 3$ and with a strictly convex boundary there are $n$ geometrically distinct orthogonal geodesic chords without self-intersections. We use a perturbation result for intersecting geodesic segments of the author and a genericity statement due to Bettiol and Giambò and existence results for orthogonal geodesic chords by Giambò, Giannoni, and Piccione. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02905 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geodesic loops and orthogonal geodesic chords without self-intersections Rademacher, Hans-Bert Differential Geometry 53C22, 58E10 We show that for a generic Riemannian metric on a compact manifold of dimension $n\ge 3$ all geodesic loops based at a fixed point have no self-intersections. We also show that for an open and dense subset of the space of Riemannian metrics on an $n$-disc with $n \ge 3$ and with a strictly convex boundary there are $n$ geometrically distinct orthogonal geodesic chords without self-intersections. We use a perturbation result for intersecting geodesic segments of the author and a genericity statement due to Bettiol and Giambò and existence results for orthogonal geodesic chords by Giambò, Giannoni, and Piccione. |
| title | Geodesic loops and orthogonal geodesic chords without self-intersections |
| topic | Differential Geometry 53C22, 58E10 |
| url | https://arxiv.org/abs/2407.02905 |