[en] A part-integral formulation in the representation of coherent states for the unitary U₂ group and U_2/1 supergroup is introduced. U₂ and U_2/1 path integrals are shown to be defined on the coset spaces U₂/U₁xU₁ and U_2/1/U_1/1xU₁, respectively. These coset appears as curved classical phase spaces. Partition functions are expressed as path integrals over these spaces. In the case when U₂ and U_2/1 are the dynamical groups, the corresponding path integrals are evaluated with the help of linear fractional transformations that appear as the group (supergroup) action in the coset space (superspace). Possible applications for quantum models are discussed. 9 refs