Comptes Rendus
no. 19-20
Geometry
Homogeneous Einstein–Randers spaces of negative Ricci curvature
[Espaces Einstein–Randers homogènes avec courbure de Ricci négative]

Présenté par : Jean-Pierre Demailly

Shaoqiang Deng1 ; Zixin Hou1
1 School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, PR China
Comptes Rendus. Mathématique, Volume 347 (2009) no. 19-20, pp. 1169-1172.

Nous prouvons que l'espace Einstein–Randers homogéne avec courbure de Ricci négative doit être Riemannian.

We prove that a homogeneous Einstein–Randers space with negative Ricci curvature must be Riemannian.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.08.006
Shaoqiang Deng 1 ; Zixin Hou 1

1 School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, PR China 
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     title = {Homogeneous {Einstein{\textendash}Randers} spaces of negative {Ricci} curvature},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1169--1172},
     publisher = {Elsevier},
     volume = {347},
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     year = {2009},
     doi = {10.1016/j.crma.2009.08.006},
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Shaoqiang Deng; Zixin Hou. Homogeneous Einstein–Randers spaces of negative Ricci curvature. Comptes Rendus. Mathématique, Volume 347 (2009) no. 19-20, pp. 1169-1172. doi : 10.1016/j.crma.2009.08.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.08.006/

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[2] D.V. Alekseevskii; B.N. Kinmel'fel'd Structure of homogeneous Riemannian manifolds with zero Ricci curvature, Functional Anal. Appl., Volume 9 (1975), pp. 95-102

[3] D. Bao; C. Robles Ricci and flag curvatures in Finsler geometry (D. Bao; R.L. Bryant; S.S. Chern; Z. Shen, eds.), A Sampler of Riemannian–Finsler Geometry, Cambridge University Press, 2004, pp. 197-260

[4] D. Bao; C. Robles; Z. Shen Zermelo navigation on Riemannian manifolds, J. Diff. Geom., Volume 66 (2004), pp. 377-435

[5] A. Besse Einstein Manifolds, Springer-Verlag, 1987

[6] S. Deng; Z. Hou The group of isometries of a Finsler space, Pacific J. Math., Volume 207 (2002), pp. 149-157

[7] S. Deng; Z. Hou Invariant Randers metrics on homogeneous Riemannian manifold, J. Phys. A: Math. Gen., Volume 37 (2004), pp. 4353-4360 (Corrigendum: J. Phys. A: Math. Gen., 39, 2006, pp. 5249-5250)

[8] Z. Shen Finsler metrics with K=0 and S=0, Canadian J. Math., Volume 55 (2003), pp. 112-132

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☆ Supported by NSFC of China (No. 10671096).

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