Projective deformations of hyperbolic Coxeter 3-orbifolds (Q438952)

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.