Geometries for Possible Kinematics
Mathematical Physics
2013-01-25 v1 General Relativity and Quantum Cosmology
math.MP
Abstract
The algebras for all possible Lorentzian and Euclidean kinematics with 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 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.
Cite
@article{arxiv.1007.3618,
title = {Geometries for Possible Kinematics},
author = {Chao-Guang Huang and Yu Tian and Xiao-Ning Wu and Zhan Xu and Bin Zhou},
journal= {arXiv preprint arXiv:1007.3618},
year = {2013}
}
Comments
40 pages, 7 figures