Deforming Euclidean cone 3–manifolds

Porti, Joan¹ ; Weiß, Hartmut²

¹ Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain
² Mathematisches Institut, Universität München, Theresienstraße 39, D-80333 München, Germany

Geometry & topology, Tome 11 (2007) no. 3, pp. 1507-1538.

Résumé

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.

Détail

DOI : 10.2140/gt.2007.11.1507

Keywords: cone 3–manifold, deformation space

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