Date of Award
2014
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Graduate Group
Mathematics
First Advisor
Wolfgang Ziller
Abstract
Recent years have seen an increase in the study of orbifolds in connection to Riemannian geometry. We connect this field to one of the fundamental questions in Riemannian geometry, namely, which spaces admit a metric of positive curvature? We give a partial classification of 4 dimensional orbifolds with positive curvature on which a circle acts by isometries. We further study the connection between orbifolds and biquotients - which in the past was one of the main techniques used to construct compact manifolds with positive curvature. In particular, we classify all orbifold biquotients of SU(3). Among those, we show that a certain 5 dimensional orbifold admits a metric of almost positive curvature. Furthermore, we provide some new results on the orbifolds SU(3)//T^2 studied by Florit and Ziller.
Recommended Citation
Yeroshkin, Dmytro, "Riemannian Orbifolds with Non-Negative Curvature" (2014). Publicly Accessible Penn Dissertations. 1510.
https://repository.upenn.edu/edissertations/1510