Integrability conditions for Killing spinors (Q800648)

The equations defining Killing spinors for supergravity are examined in detail, and it is shown that it is necessary to consider both the first and second integrability conditions. The Killing spinor-tensors, as defined by Walker and Penrose, are shown to be the spinor equivalent of conformal Killing tensors, and their relationship to the Killing spinors and spinor-vectors of supergravity is indicated.