  This paper studies the two-spinor form of the Rarita-Schwinger potentials
subject to local boundary conditions compatible with local supersymmetry. The
massless Rarita-Schwinger field equations are studied in four-real-dimensional
Riemannian backgrounds with boundary. Gauge transformations on the potentials
are shown to be compatible with the field equations providing the background is
Ricci-flat, in agreement with previous results in the literature. However, the
preservation of boundary conditions under such gauge transformations leads to a
restriction of the gauge freedom. The recent construction by Penrose of
secondary potentials which supplement the Rarita-Schwinger potentials is then
applied. The equations for the secondary potentials, jointly with the boundary
conditions, imply that the background four-geometry is further restricted to be
totally flat. The analysis of other gauge transformations confirms that, in the
massless case, the only admissible class of Riemannian backgrounds with
boundary is totally flat.
