Regenerating hyperbolic and spherical cone structures from Euclidean ones

We show that, in some cases, a Euclidean cone structure on a closed 3-manifold can be deformed into hyperbolic or spherical cone structures by moving the singular angle. We describe other deformations on the complement of the singular set by using generalized Dehn surgery parameters. In order to do that, we study the relationship between algebraic deformations of the holonomy representation and deformations of the geometric structure.