2025/03/10 by Souheib Allout, Allout, Souheib, Malek Hanounah +1 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2503.07843
The geodesic completeness of compact locally symmetric Lorentz manifolds has been established in several important cases, namely, the constant curvature, indecomposable, and Brinkmann settings. In this paper, we prove geodesic completeness in all remaining cases, thereby confirming the conjecture that all compact, locally symmetric Lorentz manifolds are geodesically complete. Along the way, we use the completeness result to give a comprehensive overview on four-dimensional compact locally symmetric Lorentz manifolds.