Proper conformal symmetries of space-times with divergence-free Weyl conformal tensor

It has been shown that a four-dimensional space-time with divergence-free Weyl conformal curvature tensor and admitting a proper conformal symmetry is locally of type O (conformally flat) or N. The latter case has been studied in terms of null sectional curvature. Finally, a physical characterization of general relativistic perfect fluid space-times with divergence-free Weyl conformal tensor has been presented and moreover it is shown that such fluid space-times admitting a proper conformal symmetry are conformally flat.