Geometries with the second Poincar\'e symmetry
  The second Poincar\'e kinematical group serves as one of new ones in addition to the known possible kinematics. The geometries with the second Poincar\'e symmetry is presented and their properties are analyzed. On the geometries, the new mechanics based on the principle of relativity with two universal constants $(c,l)$ can be established. 
Chao-Guang Huang, Yu Tian, Xiao-Ning Wu, Zhan Xu, Bin Zhou
gr-qc math-ph math.MP