Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 356

Parallel Pure Spinors on Pseudo-Riemannian Manifolds

Ines Kath

The aim of this paper is to investigate the relation between properties of projective pure spinors and the associated almost optical structures on pseudo-Riemannian spin manifolds. We prove that a projective pure spinor is parallel if and only if the associated almost optical structure is parallel. Furthermore we will calculate the curvature condition for the existence of a global parallel representative of such a projective spinor. Moreover, we specialize these results to metrics of signature $(m,m)$ and $(m+1,m)$.

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