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Travelling through sub-Riemannian spaces: the Chow-Rashevskii theorem and sub-Riemannian geodesics

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)
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: http://fse.studenttheses.ub.rug.nl/id/eprint/27926

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