تقرير
Geodesic loops and orthogonal geodesic chords without self-intersections
| العنوان: | Geodesic loops and orthogonal geodesic chords without self-intersections |
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| المؤلفون: | Rademacher, Hans-Bert |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, 53C22, 58E10 |
| الوصف: | 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 Giamb\`o and existence results for orthogonal geodesic chords by Giamb\`o, Giannoni, and Piccione. Comment: 15 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.02905 |
| رقم الأكسشن: | edsarx.2407.02905 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |