[Rigidité des espaces de Finsler à géodésiques homogènes et à courbure négative]
Nous montrons des résultats de rigidité sur les espaces de Finsler homogènes, dont les géodésiques sont des espaces homogènes à courbure non positive. En particulier, nous montrons qu'un tel espace de Finsler dont la courbure de drapeau est strictement négative doit être un espace symétrique riemannien non compact de rang un.
We prove some rigidity results on geodesic orbit Finsler spaces with non-positive curvature. In particular, we show that a geodesic orbit Finsler space with strictly negative flag curvature must be a non-compact Riemannian symmetric space of rank one.
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@article{CRMATH_2017__355_9_987_0,
author = {Xu, Ming and Deng, Shaoqiang},
title = {Rigidity of negatively curved geodesic orbit {Finsler} spaces},
journal = {Comptes Rendus. Math\'ematique},
pages = {987--990},
publisher = {Elsevier},
volume = {355},
number = {9},
year = {2017},
doi = {10.1016/j.crma.2017.09.003},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2017.09.003/}
}
TY - JOUR AU - Xu, Ming AU - Deng, Shaoqiang TI - Rigidity of negatively curved geodesic orbit Finsler spaces JO - Comptes Rendus. Mathématique PY - 2017 SP - 987 EP - 990 VL - 355 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.09.003/ DO - 10.1016/j.crma.2017.09.003 LA - en ID - CRMATH_2017__355_9_987_0 ER -
%0 Journal Article %A Xu, Ming %A Deng, Shaoqiang %T Rigidity of negatively curved geodesic orbit Finsler spaces %J Comptes Rendus. Mathématique %D 2017 %P 987-990 %V 355 %N 9 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2017.09.003/ %R 10.1016/j.crma.2017.09.003 %G en %F CRMATH_2017__355_9_987_0
Xu, Ming; Deng, Shaoqiang. Rigidity of negatively curved geodesic orbit Finsler spaces. Comptes Rendus. Mathématique, Tome 355 (2017) no. 9, pp. 987-990. doi : 10.1016/j.crma.2017.09.003. http://www.numdam.org/articles/10.1016/j.crma.2017.09.003/
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