  There is derived, for a conformally flat three-space, a family of linear
second-order partial differential operators which send vectors into tracefree,
symmetric two-tensors. These maps, which are parametrized by conformal Killing
vectors on the three-space, are such that the divergence of the resulting
tensor field depends only on the divergence of the original vector field. In
particular these maps send source-free electric fields into TT-tensors.
Moreover, if the original vector field is the Coulomb field on
$\mathbb{R}^3\backslash \lbrace0\rbrace$, the resulting tensor fields on
$\mathbb{R}^3\backslash \lbrace0\rbrace$ are nothing but the family of
TT-tensors originally written down by Bowen and York.
