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arXiv · 1007.3618

Geometries for Possible Kinematics

Chao-Guang Huang·Yu Tian·Xiao-Ning Wu·Zhan Xu·Bin Zhou
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Abstract

The algebras for all possible Lorentzian and Euclidean kinematics with $\frak{so}(3)$ isotropy except static ones are re-classified. The geometries for algebras are presented by contraction approach. The relations among the geometries are revealed. Almost all geometries fall into pairs. There exists $t \leftrightarrow 1/(\nu^2t)$ correspondence in each pair. In the viewpoint of differential geometry, there are only 9 geometries, which have right signature and geometrical spatial isotropy. They are 3 relativistic geometries, 3 absolute-time geometries, and 3 absolute-space geometries.

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Chao-Guang Huang, Yu Tian, Xiao-Ning Wu, Zhan Xu, Bin Zhou. 2010-07-21. Geometries for Possible Kinematics. https://doi.org/10.1007/s11433-012-4788-4

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