Article Dans Une Revue Geometric And Functional Analysis Année : 2024

On closed geodesics in Lorentz manifolds

Résumé

We construct a compact semi-Riemannian manifold without periodic geodesics. We also provide examples of three-dimensional Lorentz manifolds without closed geodesics. All these examples are of the form $\Gamma\backslash G$ where $G$ is a Lie group endowed with a left invariant metric and $\Gamma\subset G$ is a cocompact lattice. Unlike the locally homogeneous case, we show that a homogeneous semi-Riemannian manifold admits closed geodesics.

Dates et versions

hal-04271781 , version 1 (06-11-2023)

Identifiants

Citer

Souheib Allout, Abderrahmane Belkacem, Abdelghani Zeghib. On closed geodesics in Lorentz manifolds. Geometric And Functional Analysis, 2024, 34 (5), pp.1297-1309. ⟨10.1007/s00039-024-00675-w⟩. ⟨hal-04271781⟩
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