Existence and uniqueness theorem for convex polyhedral metrics on compact surfaces
Résumé
We state that any constant curvature Riemannian metric with conical singularities of constant sign curvature on a compact (orientable) surface $S$ can be realized as a convex polyhedron in a (Riemannian or Lorentzian) space-form. Moreover such a polyhedron is unique, up to global isometries, among convex polyhedra invariant under isometries acting on a totally umbilical surface. This general statement falls apart into 10 different cases. The cases when $S$ is the sphere are classical.
Domaines
Géométrie différentielle [math.DG]
Origine : Fichiers produits par l'(les) auteur(s)
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