Baum H., FriedrichT., Grunewald R., Kath I. Twistors and Killing spinors on Riemannian manifolds

B.G.Teubner Verlagsgesellschaft, Stuttgart- Leipzig,1991, 181 p. In this book we investigate, after an introductory section to Clifford algebras, spinors on manifolds etc., in particular solutions of the twistor equation as well as Killing spinors. New results on the construction and classification of Riemannian manifolds with real and imaginary Killing spinors, respectively, are the main subject of this book. Moreover, we consider the relations between solutions of the general twistor equation and Killing spinors.
This book is devoted to the so-called Killing and twistor spinors, special kinds of spinors on Riemannian manifolds appearing in Mathematical Physics as well as in a purely mathematical context. In the first chapter we give an introduction to Clifford algebras, spin-representation and the spinor calculus on Riemannian manifolds. Furthermore, we investigate the two natural first order differential operators on spinors, the Dirac and the Twistor operator. The main subject of the present book is the construction and the classification of Riemannian manifolds with real and imaginary Killing spinors. The results described here were obtained during the last 5 years and are presented in a systematical and complete manner in this book for the first time.