Deforming Euclidean cone 3–manifolds

Abstract

Given a closed orientable Euclidean cone 3–manifold $C$ with cone angles $\le \pi$ and which is not almost product, we describe the space of constant curvature cone structures on $C$ with cone angles $<\pi$. 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.