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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

Information

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

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