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Geometriae Dedicata

, Volume 159, Issue 1, pp 125–167 | Cite as

Projective deformations of hyperbolic Coxeter 3-orbifolds

  • Suhyoung Choi
  • Craig D. Hodgson
  • Gye-Seon LeeEmail author
Original Paper

Abstract

By using Klein’s model for hyperbolic geometry, hyperbolic structures on orbifolds or manifolds provide examples of real projective structures. By Andreev’s theorem, many 3-dimensional reflection orbifolds admit a finite volume hyperbolic structure, and such a hyperbolic structure is unique. However, the induced real projective structure on some such 3-orbifolds deforms into a family of real projective structures that are not induced from hyperbolic structures. In this paper, we find new classes of compact and complete hyperbolic reflection 3-orbifolds with such deformations. We also explain numerical and exact results on projective deformations of some compact hyperbolic cubes and dodecahedra.

Keywords

Real projective structure Orbifold Moduli space Coxeter groups Representations of groups 

Mathematics Subject Classification (2000)

57M50 57N16 53A20 53C15 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Suhyoung Choi
    • 1
  • Craig D. Hodgson
    • 2
  • Gye-Seon Lee
    • 1
    • 3
    Email author
  1. 1.Department of Mathematical SciencesKAISTDaejeonRepublic of Korea
  2. 2.Department of Mathematics and StatisticsUniversity of MelbourneMelbourneAustralia
  3. 3.BK21-Mathematical Sciences Division, Department of Mathematical SciencesSeoul National UniversitySeoulRepublic of Korea

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