  A complex orthogonal (geometric) structure on a complex manifold is a
geometric structure locally modelled on a non-degenerate quadric. One of the
first examples of such a structure on a compact manifold of dimension three was
constructed by Guillot. In this paper, we show that the same manifold carries a
family of uniformizable complex orthogonal (geometric) structures which
includes Guillot's structure; here, a structure is said to be uniformizable if
it is a quotient of an invariant open set of a quadric by a Kleinian group. We
also construct a family of uniformizable complex (geometric) projective
structures on a related compact complex manifold of dimension three.
