Shearfree congruences of null geodesies and killing tensors

In this communication, the mutual connections between quantities that are generalizations of the notion of a Killing vector field are investigated. A classification of these quantities in terms of a complex vector field_a is given. A common feature of all these quantities is that they imply the existence of a pair of shearfree geodetic null congruences. There are no explicit restrictions posed on the Ricci tensor.