Comptes Rendus
no. 9
Differential geometry
Rigidity of negatively curved geodesic orbit Finsler spaces
[Rigidité des espaces de Finsler à géodésiques homogènes et à courbure négative]

Présenté par : Jean-Michel Bismut

Ming Xu1 ; Shaoqiang Deng2
1 School of Mathematical Sciences, Capital Normal University, Beijing 100048, PR China
2 School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, PR China
Comptes Rendus. Mathématique, Volume 355 (2017) no. 9, pp. 987-990.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.09.003
Ming Xu 1 ; Shaoqiang Deng 2

1 School of Mathematical Sciences, Capital Normal University, Beijing 100048, PR China
2 School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, PR China 
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Ming Xu; Shaoqiang Deng. Rigidity of negatively curved geodesic orbit Finsler spaces. Comptes Rendus. Mathématique, Volume 355 (2017) no. 9, pp. 987-990. doi : 10.1016/j.crma.2017.09.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.09.003/

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[14] M. Xu; S. Deng Normal homogeneous Finsler spaces, Transform. Groups (2017) (published online) | DOI

[15] M. Xu; S. Deng; L. Huang; Z. Hu Even dimensional homogeneous Finsler spaces with positive flag curvature, Indiana Univ. Math. J., Volume 66 (2017), pp. 949-972

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