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Souheib Allout

Publications and source records attributed to Souheib Allout.

5 recordsLinked to original sources
arXiv2026

Completeness of compact Locally symmetric Lorentz manifolds

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.

math.DG↗
arXiv2025

On homogeneous 3-dimensional spacetimes: focus on plane waves

We revisit the classification of Lorentz homogeneous spaces of dimension $3$, and relax usual completeness assumptions. In particular, non-unimodular elliptic plane waves, and only them, are neither locally symmetric nor locally isometric to a left-invariant Lorentz metric on a $3$-dimensional Lie group. We characterize homogeneous plane waves in dimension $3$, and prove they are non-extendable, and geodesically complete only if they are symmetric. Finally, only one non-flat plane wave has a compact model.

math.DG↗
arXiv2024

On contact mapping classes of prequantizations

We present examples of prequantizations over integral symplectic manifolds which admit infinitely many smoothly trivial contact mapping classes. These classes are given by the connected components of the strict contactomorphism group which project to the identity component of the symplectomorphism group of the base manifold. Along the way, we study the lifting problem of symplectomorphisms of the base manifold to strict contactomorphisms of the prequantization.

math.SG↗