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Positive definite Minkowski Lie algebras and bi-invariant Finsler metrics on Lie groups

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Abstract

In this paper, we introduce the notion of a Minkowski Lie algebra, which is the natural generalization of the notion of a real quadratic Lie algebra (metric Lie algebra). We then study the positive definite Minkowski Lie algebras and obtain a complete classification of the simple ones. Finally, we present some applications of our results to Finsler geometry and give a classification of bi-invariant Finsler metrics on Lie groups.

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Authors and Affiliations

  1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, People’s Republic of China

    Shaoqiang Deng & Zixin Hou

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  1. Shaoqiang Deng
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  2. Zixin Hou
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Correspondence to Shaoqiang Deng.

Additional information

This work was supported by NSFC (No.10671096) and NCET of China.

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Deng, S., Hou, Z. Positive definite Minkowski Lie algebras and bi-invariant Finsler metrics on Lie groups. Geom Dedicata 136, 191–201 (2008). https://doi.org/10.1007/s10711-008-9284-7

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  • DOI: https://doi.org/10.1007/s10711-008-9284-7

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