  We study the gravitational wave memory effect in spacetimes related to flat
space by a conformal transformation. The discussion is general but the
gravitational wave length scale is assumed to be small compared with the
background curvature radius. The general formulas are applied to
Friedmann-Robertson-Walker metrics of all spatial curvatures. The effect of new
terms stemming from spatial curvature is potentially detectable in future
gravitational wave measurements.
