  We formulate the necessary conditions for the integrability of a certain
family of Hamiltonian systems defined in the constant curvature two-dimensional
spaces. Proposed form of potential can be considered as a counterpart of a
homogeneous potential in flat spaces. Thanks to this property Hamilton
equations admit, in a general case, a particular solution. Using this solution
we derive necessary integrability conditions investigating differential Galois
group of variational equations.
