Deforming Euclidean cone 3–manifolds

Abstract

Given a closed orientable Euclidean cone 3-manifold C with cone angles and which is not almost product, we describe the space of constant curvature cone structures on C with cone angles < . We establish a regeneration result for such Euclidean cone manifolds into spherical or hyperbolic ones and we also deduce global rigidity for Euclidean cone structures.