Javascript must be enabled for the correct page display

An exploration of sub-Riemannian Orbifolds

Koster, Oscar (2023) An exploration of sub-Riemannian Orbifolds. Master's Thesis / Essay, Mathematics.


Download (2MB) | Preview
[img] Text
Restricted to Registered users only

Download (132kB)


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)
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

Actions (login required)

View Item View Item