  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.
