Projective deformations of hyperbolic Coxeter 3-orbifolds
type: Item
instance of: scholarly article
title: Projective deformations of hyperbolic Coxeter 3-orbifolds
zbMATH Open document ID: 1266.57012
author: Suhyoung Choi
author: Craig Hodgson
author: Gye-Seon Lee
published in: Geometriae Dedicata
publication date: 2012-07-31T00:00:00Z
full work available at URL: https://arxiv.org/abs/1003.4352
review text: Hyperbolic structures on orbifolds or manifolds provide examples of real projective structures. By Mostow-Prasad rigidity, the hyperbolic structure of a finite volume hyperbolic orbifold, of dimension greater than two, is unique. However, there are cases where the associated real projective structure has a non-trivial deformation space. The authors find new classes of hyperbolic 3-orbifolds where the induced real projective structure deforms into a family of real projective structures that are not induced from hyperbolic structures. Let \(\hat{P}\) be an orbifold whose underlying space is an ideal 3-dimensional hyperbolic polyhedron with dihedral angles are all equal to \(\pi/3\), whose singular locus is its boundary and which is not a tetrahedron. The main result is that the hyperbolic point in the deformation space of real projective structures of \(\hat{P}\) is a smooth 6-dimensional manifold. The authors also describe computational results on the projective deformation space of certain compact hyperbolic cubes and dodecahedra.
reviewed by: Ilesanmi Adeboye
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 57N16
Mathematics Subject Classification ID: 53A20
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 6062605
zbMATH Keywords: real projective structure
zbMATH Keywords: orbifold
zbMATH Keywords: Coxeter groups
MaRDI profile type: Publication
OpenAlex ID: W2033215601
arXiv ID: 1003.4352
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DOI: 10.1007/S10711-011-9650-8
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description: scientific article; zbMATH DE number 6062605