RIGIDITY AND DEGENERATION OF 3-DIMENSIONAL HYPERBOLIC CONE STRUCTURES (Geometry of discrete groups and hyperbolic spaces)

Abstract

In this note, we survey rigidity of hyperbolic cone structures and give an example of degeneration with decreasing cone angles. This example is constructed by gluing four copies of a certain polyhedron. We can explicitly describe the isometry types of such hyperbolic polyhedra. Furthermore, we introduce a generalization of cone structure to avoid intersection of cone loci.