Quasi-fuchsian structures on hyperbolic 3-manifolds admitting a decomposition into ideal tetrahedra
This work aims at quasi-Fuchsian structures on hyperbolic 3-manifolds. They were first studied by \textit{W. P. Thurston} [The geometry and topology of three-manifolds, Princeton Univ. Maths. Dept. Notes (1979)] where he started with a hyperbolic link \(L\) in \(S^3\). He had shown that infinitely many of the manifolds obtained by Dehn surgery on \(L\) admit complete hyperbolic structures. In this work some local problems proposed in an earlier paper are adressed and it is shown that for hyperbolic 3-manifolds \(M\) obtained from Thurston's construction, the structures in an open neighbourhood of the hyperbolic structure can be characterized by some similarity structures on the links of the components of \(L\) satisfying certain conditions. This is done without using extra parameters.
scientific article; zbMATH DE number 938532
scientific article