Koster, Oscar (2023) An exploration of sub-Riemannian Orbifolds. Master's Thesis / Essay, Mathematics.
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Abstract
Orbifolds and sub-Riemannian manifolds are generalizations of the concept of manifold. Orbifolds generalize manifolds by incorporating singularities, while sub-Riemannian manifolds exclude specific geodesics and restrict movement to chosen subsets. In this thesis we discuss the possibility to define a sub-Riemannian structure on an orbifold. First, we sketch a method to define sub-Riemannian structure on the regular part of an orbifold, similar to the known construction of sub-Riemannian structures on lens spaces. However, problems for the horizontal distribution occur around the singularities on the orbifold. It turns out that a sub-Riemannian distribution on an orbifold is well-defined around the singular points if it is equivariant with respect to the actions on the orbifold. As a result we define sub-Riemannian structures on orbifolds obtained by reflections, rotation and the (p, q)-Hopf action and find geodesics in these cases. We also sketch an extension of a result by Herr, to find a sub-Riemannian structure on any closed cyclic 3-orbifolds.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Seri, M. |
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 07 Aug 2023 12:45 |
| Last Modified: | 09 Aug 2023 11:00 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/30979 |
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