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| Main Authors: | , , |
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| 格式: | Preprint |
| 出版: |
2025
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| 主題: | |
| 在線閱讀: | https://arxiv.org/abs/2510.25585 |
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書本目錄:
- We completely classify the bijections of the Thurston geometries that preserve geodesics as sets. For Riemannian manifolds that satisfy a certain technical condition, we prove that a totally geodesic subset is a submanifold. We also classify the geodesic-preserving bijections of the Euclidean cylinder $\mathbb{S}^1 \times \mathbb{R}$ and the bijections of the hyperbolic plane $\mathbb{H}^2$ that preserve constant curvature curves.