We report a beginning in a project to determine the consequences of the following assumption, "that a physical theory in flat space is obtainable as the limit of a physical theory in a curved space." Because of the absence of groups of motion in general curved spaces, we discuss only the case of constant curvature. Then operators of angular and linear momentum exist, and we show that the interesting irreducible unitary representations of the group of motions reduce very simply to those of the inhomogeneous Lorentz group in the limit of zero curvature.