Abstract
Two flat-space transverse-traceless tensor operators can be used to construct initial data for numerical solutions of the gravitational field equations. One of these operators is related to the conformal curvature 3-tensor and is shown to exist in a large class of nonflat 3-spaces. The second operator enjoys no such liberty. Important applications to gravitational wave scattering are suggested. It is argued that the number of operators available on a particular 3-space is related to the number of gravitational field modes that are excited in the space.