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KILLING FRAMES AND S-CURVATURE OF HOMOGENEOUS FINSLER SPACES*

Part of: Lie groups Global differential geometry

Published online by Cambridge University Press:  22 December 2014

MING XU  and
SHAOQIANG DENG
MING XU
Affiliation:
College of Mathematics, Tianjin Normal University, Tianjin 300387, P.R. China
SHAOQIANG DENG*
Affiliation:
School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P.R. China, E-mail: dengsq@nankai.edu.cn
*
†Corresponding author. e-mail: dengsq@nankai.edu.cn
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Abstract

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In this paper, we first deduce a formula of S-curvature of homogeneous Finsler spaces in terms of Killing vector fields. Then we prove that a homogeneous Finsler space has isotropic S-curvature if and only if it has vanishing S-curvature. In the special case that the homogeneous Finsler space is a Randers space, we give an explicit formula which coincides with the previous formula obtained by the second author using other methods.

MSC classification

Primary: 22E46: Semisimple Lie groups and their representations
Secondary: 53C30: Homogeneous manifolds
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 57 , Issue 2 , May 2015 , pp. 457 - 464
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

Footnotes

*

Supported by NSFC (no. 11271216, 11271198, 11221091), Doctor fund of Tianjin Normal University (no. 52XB1305) and SRFDP of China

References

REFERENCES

1.Bao, D., Chern, S. S. and Shen, Z., An introduction to Riemann-Finsler geometry (Springer-Verlag, New York, USA, 2000).CrossRefGoogle Scholar
2.Bao, D. and Robles, C., Ricci and flag curvatures in Finsler geometry, in A sampler of Riemannian-Finsler geometry (Bao, D., Bryant, R. L., Chern, S. S. and Shen, Z., Editors) (Cambridge University Press, 2004), 197–260.Google Scholar
3.Chern, S. S. and Shen, Z., Riemann-Finsler Geometry (World Scientific Publishers, 2004).Google Scholar
4.Deng, S., Homogeneous Finsler spaces, Springer Monographs in Mathematics (Springer, New York, USA, 2012).Google Scholar
5.Deng, S., The S-curvature of homogeneous Randers spaces, Differ. Geom. Appl. 27 (1) (2009), 75–84.Google Scholar
6.Deng, S. and Hou, Z., The group of isometries of a Finsler space, Pacific J. Math. 207 (1) (2002), 149–157.Google Scholar
7.Deng, S. and Wang, X., The S-curvature of homogeneous (α,β)-metrics, Balkan J. Geom. Appl. 15 (2) (2010), 39–48.Google Scholar
8.Shen, Z., Volume comparison and its applications in Riemann-Finsler geometry, Adv. Math. 128 (2) (1997), 306–328.Google Scholar
9.Shen, Z., Differential geometry of sprays and Finsler spaces (Kluwer, Dordrent, 2001).CrossRefGoogle Scholar