We show that a compact Lorentzian locally symmetric space is geodesically complete if the Lorentzian factor in the local de Rham–Wu decomposition is of Cahen–Wallach type or if the maximal flat factor is one-dimensional and time-like. Our proof uses a recent result by Mehidi and Zeghib and an earlier result by Romero and Sánchez.
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Keywords: Lorentzian manifolds, Lorentzian symmetric spaces, geodesic completeness
Thomas Leistner 1; Thomas Munn 2
@article{CRMATH_2023__361_G4_819_0, author = {Thomas Leistner and Thomas Munn}, title = {Completeness of certain compact {Lorentzian} locally symmetric spaces}, journal = {Comptes Rendus. Math\'ematique}, pages = {819--824}, publisher = {Acad\'emie des sciences, Paris}, volume = {361}, year = {2023}, doi = {10.5802/crmath.449}, language = {en}, }
Thomas Leistner; Thomas Munn. Completeness of certain compact Lorentzian locally symmetric spaces. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 819-824. doi : 10.5802/crmath.449. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.449/
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