Deformations of Hyperbolic Structures without the Completeness Condition

Abstract

In the general case of deformations without the completeness condition we will show that the complex dimensionality of the space Def* $M^3$ is equal to the nunber of isolated ends of the three-manifold $M^3$. For $n\ge 4$ there exists a strong rigidity of deformations, similar to the rigidity of complete hyperbolic structures.