Dissertation, University of California - Los Angeles, January 1, 1992, pages 1-57.
NOTE: At the time of publication, the author Joseph Ernest Borzellino was not yet affiliated with Cal Poly.
We investigate generalizations of many theorems of Riemannian geometry to Riemannian orbifolds. Basic definitions and many examples are given. It is shown that Riemannian orbifolds inherit a natural stratified length space structure. A version of Toponogov's triangle comparison theorem for Riemannian orbifolds is proven. A structure theorem for minimizing curves shows that such curves cannot pass through the singular set. A generalization of the Bishop relative volume comparison theorem is presented. The maximal diameter theorem of Cheng is generalized. A finiteness result and convergence result is proven for good Riemannian orbifolds, and the existence of a closed geodesic is shown for non-simply connected Riemannian orbifolds.
1992 Joseph Ernest Borzellino.