Affine deformations of quasi-divisible convex cones - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Proceedings of the London Mathematical Society Année : 2023

Affine deformations of quasi-divisible convex cones

Xin Nie
  • Fonction : Auteur
  • PersonId : 1045654
Andrea Seppi

Résumé

For any subgroup of SL(3,R)xR^3 obtained by adding a translation part to a subgroup of SL(3,R) which is the fundamental group of a finite-volume convex projective surface, we first show that under a natural condition on the translation parts of parabolic elements, the affine action of the group on R^3 has convex domains of discontinuity that are regular in a certain sense, generalizing a result of Mess for globally hyperbolic flat spacetimes. We then classify all these domains and show that the quotient of each of them is an affine manifold foliated by convex surfaces with constant affine Gaussian curvature. The proof is based on a correspondence between the geometry of an affine space endowed with a convex cone and the geometry of a convex tube domain. As an independent result, we show that the moduli space of such groups is a vector bundle over the moduli space of finite-volume convex projective structures, with rank equaling the dimension of the Teichmüller space.
Fichier principal
Vignette du fichier
Xin2_arxiv.pdf (602.83 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-03000891 , version 1 (12-11-2020)

Identifiants

Citer

Xin Nie, Andrea Seppi. Affine deformations of quasi-divisible convex cones. Proceedings of the London Mathematical Society, 2023, ⟨10.1112/plms.12537⟩. ⟨hal-03000891⟩
36 Consultations
42 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More