We characterize certain CR structures of arbitrary codimension (different
from 3, 4 and 5) on Riemannian Spinc manifolds by the existence of a
Spinc structure carrying a strictly partially pure spinor field.
Furthermore, we study the geometry of Riemannian Spinc 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in prescribed directions.Comment: This paper has been withdrawn by the author.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