  In the complex-Riemannian framework we show that a conformal manifold
containing a compact, simply-connected, null-geodesic is conformally flat. In
dimension 3 we use the LeBrun correspondence, that views a conformal 3-manifold
as the conformal infinity of a selfdual four-manifolds. We also find a relation
between the conformal invariants of the conformal infinity and its ambient.
