  Ray nil-affine geometries are defined on nilpotent spaces. They occur in
every parabolic geometry and in those cases, the nilpotent space is an open
dense subset of the corresponding flag manifold. We are interested in closed
manifolds having a ray nil-affine structure. We show that under a rank one
condition on the isotropy, closed manifolds are either complete or their
developing map is a cover onto the complement of a nil-affine subspace. We
prove that if additionally there is a parallel volume or if the automorphism
group acts non properly then closed manifolds are always complete.This paper is
a sequel to a previous work on ray manifolds in affine geometry.

Differential Geometry;Geometric Topology