Spacetimes with cosmological constant and a conformal Killing field have constant curvature

The assumption that a spacetime possesses a conformal Killing field which is not a Killing field can be very restrictive. The authors examine the effect of this assumption on vacuum solutions of Einstein's equation with cosmological constant. It is shown that all such solutions have constant curvature and are therefore either de Sitter spacetimes or anti-de Sitter spacetimes, depending on the sign of the cosmological constant.