  Modified and deformed relativistic kinematics are considered to capture
effects from quantum gravity on the behavior of point particles. The idea is
that higher-energetic particles probe spacetime at smaller scales and start to
be subject to quantum gravity effects. This can be modeled by a momentum
dependent spacetime geometry, respectively by a curved momentum space. For flat
spacetime this idea is well understood. However, if one wants to relate this
idea to phenomenology of quantum gravity in cosmic and astrophysical
observations, it is necessary to implement deformed relativistic kinematics
consistently on curved spacetimes. We conjecture a precise way to achieve this
by identifying a quantum deformation of a given curved spacetime geometry in
terms of a maximally symmetric momentum space metric on curved spacetime.
