Reference - Riemannian Orbifolds

Question

I am looking for papers or textbooks talking about the various analog theorems of Riemannian Geometry of Manifolds to Riemannian Orbifolds like Toponogovs Theorem, Bonnet-Myers, Gauss Bonnet etc.

So far I have in mind:

1. P. Scott - "The geometries of 3-manifolds"
2. W. P. Thurston - "The Geometry and Topology of Three-Manifolds"
3. Borzellino's various papers on Riemannian Orbifolds
4. Satake's papers on the originally called V-manifolds

What other textbooks or papers do you suggest on this topic?

Answer 1

I have gathered all suggestions in the following list:

1. P. Scott -The geometries of 3-manifolds
2. W. P. Thurston - The Geometry and Topology of Three-Manifolds
3. J.E. Borzellino - PhD Thesis
4. I. Satake - On a generalization of the notion of manifold
5. J. Ratcliffe - Foundations of Hyperbolic Manifolds
6. M. Boileau, S. Maillot, J. Porti - Three-Dimensional Orbifolds and their Geometric Structures
7. B. Kleiner, J.Lott - Geometrization of Three-Dimensional Orbifolds via Ricci Flow
8. D. Cooper, C.D. Hodgson, S.P. Kerckhoff - Three-dimensional Orbifolds and Cone-Manifolds

Answer 2

More modern references are Three-Dimensional Orbifolds and their Geometric Structures and Geometrization of Three-Dimensional Orbifolds via Ricci Flow. Both mostly deal with 3-dimensional case, but cover basics as well. In addition, you should note that every Riemannian orbifold, when treated as a length metric space, is (locally) an Alexandrov space: its curvature (locally) is bounded above and below in the sense of Alexandrov. In particular, comparison theorems will hold. Once you have those, much of the rest of the standard Riemannian results will hold as well. Take a look here: "A Course in Metric Geometry".