  A closed affine manifold is a closed manifold with coordinate patches into
affine space whose transition maps are restrictions of affine automorphisms.
Such a structure gives rise to a local diffeomorphism from the universal cover
of the manifold to affine space that is equivariant with respect to a
homomorphism from the fundamental group to the group of affine automorphisms.
The local diffeomorphism and homomorphism are referred to as the developing map
and holonomy respectively. In the case where the linear holonomy preserves a
common vector, certain `large' open subsets upon which the developing map is a
diffeomorphism onto its image are constructed. A modified proof of the fact
that a radiant manifold cannot have its fixed point in the developing image is
presented. Combining these results, this paper addresses the non-existence of
certain closed affine manifolds whose holonomy leaves invariant an affine line.
Specifically, if the affine holonomy acts purely by translations on the
invariant line, then the developing image cannot meet this line.
