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
Leistner, Thomas 1 ; Munn, Thomas 2
CC-BY 4.0
@article{CRMATH_2023__361_G4_819_0,
author = {Leistner, Thomas and Munn, Thomas},
title = {Completeness of certain compact {Lorentzian} locally symmetric spaces},
journal = {Comptes Rendus. Math\'ematique},
pages = {819--824},
year = {2023},
publisher = {Acad\'emie des sciences, Paris},
volume = {361},
number = {G4},
doi = {10.5802/crmath.449},
language = {en},
url = {https://www.numdam.org/articles/10.5802/crmath.449/}
}
TY - JOUR AU - Leistner, Thomas AU - Munn, Thomas TI - Completeness of certain compact Lorentzian locally symmetric spaces JO - Comptes Rendus. Mathématique PY - 2023 SP - 819 EP - 824 VL - 361 IS - G4 PB - Académie des sciences, Paris UR - https://www.numdam.org/articles/10.5802/crmath.449/ DO - 10.5802/crmath.449 LA - en ID - CRMATH_2023__361_G4_819_0 ER -
%0 Journal Article %A Leistner, Thomas %A Munn, Thomas %T Completeness of certain compact Lorentzian locally symmetric spaces %J Comptes Rendus. Mathématique %D 2023 %P 819-824 %V 361 %N G4 %I Académie des sciences, Paris %U https://www.numdam.org/articles/10.5802/crmath.449/ %R 10.5802/crmath.449 %G en %F CRMATH_2023__361_G4_819_0
Leistner, Thomas; Munn, Thomas. Completeness of certain compact Lorentzian locally symmetric spaces. Comptes Rendus. Mathématique, Tome 361 (2023) no. G4, pp. 819-824. doi: 10.5802/crmath.449
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