Spinorial Characterization of CR Structures, I

Abstract

We characterize certain CR structures of arbitrary codimension (different from 3, 4 and 5) on Riemannian Spin$^c$ manifolds by the existence of a Spin$^c$ structure carrying a strictly partially pure spinor field. Furthermore, we study the geometry of Riemannian Spin$^c$ manifolds carrying a strictly partially pure spinor which satisfies the generalized Killing equation in prescribed directions.Comment: This paper has been withdrawn by the author. All results have been changed because we extended them to all co-dimensions. We changed completely the pape