English

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 so(3)\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 t1/(ν2t)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.

Keywords

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

R2 v1 2026-06-21T15:50:53.447Z