  We study conformal Fefferman-Lorentz manifolds introduced by Fefferman. To do
so, we introduce Fefferman-Lorentz structure on (2n+2)-dimensional manifolds.
By using causal conformal vector fields preserving that structure, we shall
establish two theorems on compact Fefferman-Lorentz manifolds: One is the
coincidence of vanishing curvature between Weyl conformal curvature tensor of
Fefferman metrics on a Lorentz manifold $S^1\times N$ and Chern-Moser curvature
tensor on a strictly pseudoconvex CR-manifold $N$. Another is the analogue of
the conformal rigidity theorem of Obata and Lelong to the compact
Fefferman-Lorentz manifolds admitting noncompact closed causal conformal
Fefferman-Lorentz transformations.
