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Twistors and Killing spinors on Riemannian manifolds. (English) Zbl 0734.53003
Teubner-Texte zur Mathematik, 124. Stuttgart etc.: B. G. Teubner Verlagsgesellschaft. 180 p. DM 29.00/pbk (1991).
As its title indicates the book is devoted to twistors and Killing spinors on Riemannian manifolds. It describes in a detailed and systematic manner - usually giving complete proofs - the results obtained in the last five years by the authors. Thus, the book is a most welcome addition to the literature, particularly since it includes not only the expected algebraic and topological details, but also the associated differential-geometric applications of these results. Contents include chapters devoted to: An introduction to Killing and twistor spinors, The properties of twistor spinors, A survey of twistor theory, Odd- dimensional Riemannian manifolds with real Killing spinors, Even- dimensional Riemannian manifolds with real Killing spinors, Manifolds with parallel spinor fields, and Riemannian manifolds with imaginary Killing spinors, and an exhaustive set of references. The book makes little contact with theoretical physics, but its readability and rich content should make it required reading for differential geometers, mathematical/theoretical physicists, and topologists.

##### MSC:
 53-02 Research exposition (monographs, survey articles) pertaining to differential geometry 53C27 Spin and Spin$${}^c$$ geometry 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C56 Other complex differential geometry