Geodesic
On Flag Curvature of Homogeneous Randers Spaces
Canadian journal of mathematics, Tome 65 (2013) no. 1, pp. 66-81

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DOI

In this paper we give an explicit formula for the flag curvature of homogeneous Randers spaces of Douglas type and apply this formula to obtain some interesting results. We first deduce an explicit formula for the flag curvature of an arbitrary left invariant Randers metric on a two-step nilpotent Lie group. Then we obtain a classification of negatively curved homogeneous Randers spaces of Douglas type. This results, in particular, in many examples of homogeneous non-Riemannian Finsler spaces with negative flag curvature. Finally, we prove a rigidity result that a homogeneous Randers space of Berwald type whose flag curvature is everywhere nonzero must be Riemannian.
DOI : 10.4153/CJM-2012-004-6
Mots-clés : 22E46, 53C30, homogeneous Randers manifolds, flag curvature, Douglas spaces, two-step nilpotent Liegroups 
Deng, Shaoqiang; Hu, Zhiguang. On Flag Curvature of Homogeneous Randers Spaces. Canadian journal of mathematics, Tome 65 (2013) no. 1, pp. 66-81. doi: 10.4153/CJM-2012-004-6
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     title = {On {Flag} {Curvature} of {Homogeneous} {Randers} {Spaces}},
     journal = {Canadian journal of mathematics},
     pages = {66--81},
     year = {2013},
     volume = {65},
     number = {1},
     doi = {10.4153/CJM-2012-004-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2012-004-6/}
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