Krijgsheld, Henrieke (2022) Travelling through sub-Riemannian spaces: the Chow-Rashevskii theorem and sub-Riemannian geodesics. Bachelor's Thesis, Mathematics.
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Abstract
This thesis studies paths in sub-Riemannian spaces. The Chow-Rashevskii theorem is proved, which states the existence of an admissible curve connecting any two points in a sub-Riemannian manifold, and states that the sub-Riemannian distance defines a metric space on the manifold, whose topology is the same as the original manifold topology. Additionally, the existence of length-minimizing curves, given some assumptions, is proved. Finally, a sub-Riemannian Hamiltonian is derived using Pontryagin extremals, and it is proven that the solutions to the Hamiltonian system project to geodesics.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Seri, M. and Martynchuk, N. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 15 Jul 2022 12:52 |
| Last Modified: | 15 Jul 2022 12:52 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/27926 |
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