Projective deformations of hyperbolic Coxeter 3-orbifolds
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...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
August 2012
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| In: |
Geometriae dedicata
Year: 2012, Volume: 159, Issue: 1, Pages: 125-167 |
| ISSN: | 1572-9168 |
| DOI: | 10.1007/s10711-011-9650-8 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1007/s10711-011-9650-8 Verlag, Volltext: https://link.springer.com/article/10.1007/s10711-011-9650-8 
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| Author Notes: | Suhyoung Choi, Craig D. Hodgson, Gye-Seon Lee |
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| 520 | |a 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. | ||
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