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arXiv · 2410.03260

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

Martin Mion-Mouton
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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.

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Martin Mion-Mouton. 2025-12-01. Rigidity of singular de-Sitter tori with respect to their lightlike bi-foliation. https://arxiv.org/abs/2410.03260

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