On the Flag Curvature of Invariant Randers Metrics

被引：0
作者：
Hamid Reza Salimi Moghaddam
机构：
[1] Shahrood University of Technology,Department of Mathematics
来源：
Mathematical Physics, Analysis and Geometry | 2008年 / 11卷
关键词：
Invariant metric; Flag curvature; Randers space; Homogeneous space; Lie group; 22E60; 53C60; 53C30;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In the present paper, the flag curvature of invariant Randers metrics on homogeneous spaces and Lie groups is studied. We first give an explicit formula for the flag curvature of invariant Randers metrics arising from invariant Riemannian metrics on homogeneous spaces and, in special case, Lie groups. We then study Randers metrics of constant positive flag curvature and complete underlying Riemannian metric on Lie groups. Finally we give some properties of those Lie groups which admit a left invariant non-Riemannian Randers metric of Berwald type arising from a left invariant Riemannian metric and a left invariant vector field.
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页码：1 / 9
页数：8
相关论文
共 24 条
[1]  
Adams J.F.(1960)On the non-existence of elements of Hopf invariant one Ann. Math. 72 20-104
[2]  
Bao D.(2004)Randers space forms Period. Math. Hungar. 48 3-15
[3]  
Bao D.(2003)On randers spaces of constant flag curvature Rep. Math. Phys. 51 9-42
[4]  
Robles C.(2002)Finsler metrics of constant positive curvature on lie group J. Lond. Math. Soc. 66 453-467
[5]  
Bao D.(2003)Randers manifolds of positive constant curvature Internat. J. Math. Math. Sci. 2003 1155-1165
[6]  
Shen Z.(2007)Invariant metrics with nonnegative curvature on compact lie groups Canad. Math. Bull. 50 24-34
[7]  
Bejancu A.(2006)Flag curvature of invariant Randers metrics on homogeneous manifolds J. Phys. A: Math. Gen. 39 3319-3324
[8]  
Farran H.R.(2006)Induced invariant Finsler metrics on quotient groups Balkan J. Geom. Appl. 11 73-79
[9]  
Brown N.(2004)Invariant Finsler metrics on homogeneous manifolds J. Phys. A: Math. Gen. 37 8245-8253
[10]  
Finck R.(2004)Invariant Randers metrics on homogeneous Riemannian manifolds J. Phys. A: Math. Gen. 37 4353-4360
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