Twistor spinors on conformally flat manifolds (Q1362388)

In [\textit{W. Kühnel} and \textit{H.-B. Rademacher}, Int. J. Math. 5, 877-895 (1994; Zbl 0818.53054)] the authors proved that if a Riemannian spin manifold admits a twistor-spinor with zeros and a nontrivial conformal field, then the manifold is conformally flat. The present paper establishes the converse statement, and provides a description of conformally flat manifolds which admit twistor-spinors with zeros and a nontrival conformal field. Contents include: an introduction; conformal invariance of twistor-spinors; and conformally flat manifolds with twistor-spinors.