Completeness of certain compact Lorentzian locally symmetric spaces

Thomas Leistner; Thomas Munn

doi:10.5802/crmath.449

Géométrie et Topologie

Completeness of certain compact Lorentzian locally symmetric spaces

Thomas Leistner ¹ ; Thomas Munn ²

¹ School of Mathematical Sciences, University of Adelaide, SA 5005, Australia
² Lund University, Faculty of Science, Centre for Mathematical Sciences, Box 118, 22100 Lund, Sweden

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 819-824.

Résumé

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.

Reçu le : 2022-11-15
Révisé le : 2022-11-22
Accepté le : 2022-11-23
Publié le : 2023-05-11

DOI : 10.5802/crmath.449

Classification : 53C50, 53C35
Mots clés : Lorentzian manifolds, Lorentzian symmetric spaces, geodesic completeness

Affiliations des auteurs :

Thomas Leistner ¹ ; Thomas Munn ²

¹ School of Mathematical Sciences, University of Adelaide, SA 5005, Australia
² Lund University, Faculty of Science, Centre for Mathematical Sciences, Box 118, 22100 Lund, Sweden

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Completeness of certain compact {Lorentzian} locally symmetric spaces},
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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/

Bibliographie
Cité par

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