Collective classical motion on hyperbolic spacetimes of any dimensions

The geodesics equations on de Sitter and anti-de Sitter spacetimes of any dimensions, are the starting point for deriving the general form of the Boltzmann equation in terms of conserved quantities. The simple equation for the non-equilibrium Marle and Anderson-Witting models are derived and the distributions of the Boltzmann-Marle model on these manifolds are written down first in terms of conserved quantities and then as functions of canonical variables.