1. Introduction. Let M be a closed oriented 3-manifold admitting a hyperbolic struc-ture. It is well-known by Mostow rigidity that the deformation space of hyperbolic structures on M is trivial. However, viewing the hyperbolic structure as a flat conformal (or Mobius) structure and considering the space ^(M) of flat conformal structures on M, it is no longer necessarily true that #(M) is trivial. Indeed, many examples of manifolds M have been constructed where (M) is not trivial, see [1], [3], [6] and [10] for example. In most of these cases, not much is known about the space (M) except for a lower bound for the dimension in terms of the number of non-intersecting totally geodesic hypersur-faces on M.
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