* Astronomy

Title: Geometries for Possible Kinematics
Authors: Chao-Guang Huang, Yu Tian, Xiao-Ning Wu, Zhan Xu, Bin Zhou

The algebras for all possible Lorentzian and Euclidean kinematics with 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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