Conformal vector fields and conformal-type collineations in space-times

Some restrictions on the existence of homothetic and conformal vector fields in space-times which already admit some Killing symmetry are established, In particular, the behaviour of Weyl invariants and the nature of the Petrov type of the Weyl tensor along the integral curves of conformal vector fields are studied. This results in important restrictions between conformal vector fields and Killing orbits. A brief remark is made on Weyl collineations.