2015/01/02 by Suhyoung Choi, Choi, Suhyoung · 1 citation
Mathematics · #53C15 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Primary 57M50 #Secondary 53A20 #math.GT #msc:53A20 #msc:53C15 #msc:57M50
paper · pdf · doi:10.48550/arxiv.1501.00352
89 pages, 5 figures, This is the second part of the paper "A classification of radial and totally geodesic ends of properly convex real projective orbifolds", arXiv:1304.1605, which the author is dividing into three parts
openalex publication_date 2015/01/02 · arxiv created 2015/07/02 · arxiv updated 2015/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Real projective structures on n-orbifolds are useful in understanding the space of representations of discrete groups into SL(n+1, ℝ) or PGL(n+1, ℝ). A recent work shows that many hyperbolic manifolds deform to manifolds with such structures not projectively equivalent to the original ones. The purpose of this paper is to understand the structures of properly convex ends of real projective n-dimensional orbifolds. In particular, these have the radial or totally geodesic ends. For this, we will study the natural conditions on eigenvalues of holonomy representations of ends when these ends are manageably understandable. In this paper, we only study the properly convex ends. The main techniques are the Vinberg duality and a generalization of the work of Goldman, Labourie, and Margulis on flat Lorentzian 3-manifolds. Finally, we show that a noncompact strongly tame properly convex real projective orbifold with generalized lens-type or horospherical ends satisfying some topological conditions always has a strongly irreducible holonomy group.