Rigidity of singular de-Sitter tori with respect to their lightlike bi-foliation

Abstract

In this paper, we introduce a natural notion of constant curvature Lorentzian surfaces with conical singularities, and provide a large class of examples of such structures. We moreover initiate the study of their global rigidity, by proving that de-Sitter tori with a single singularity of a fixed angle are determined by the topological equivalence class of their lightlike bi-foliation. While this is reminiscent of Troyanov's uniformization results on Riemannian surfaces with conical singularities, the rigidity will come from topological dynamics in the Lorentzian case.

Revision after referee process. 78 pages