  We consider an aggregation model that consists of an active transport
equation for the macroscopic population density, where the velocity has a
nonlocal functional dependence on the density, modelled via an interaction
potential. We set up the model on general Riemannian manifolds and provide a
framework for constructing interaction potentials which lead to equilibria that
are constant on their supports. We consider such potentials for two specific
cases (the two-dimensional sphere and the two-dimensional hyperbolic space) and
investigate analytically and numerically the long-time behaviour and
equilibrium solutions of the aggregation model on these manifolds. Equilibria
obtained numerically with other interaction potentials are also presented.
