 Locally all pure spinors can be written in the same form, depending on an integer "k", the B-field 2-form "B", a nondegenerate symplectic form ω and a "k"-form Ω.In a local neighborhood of any point a pure spinor Φ which generates the canonical bundle may always be put in the form

where Ω is decomposable as the wedge product of one-forms.Define the subbundle E of the complexified tangent bundle formula_59 to be the projection of the holomorphic subbundle L of formula_51 to formula_61 In the definition of a generalized almost complex structure we have imposed that the intersection of L and its conjugate contains only the origin, otherwise they would be unable to span the entirety of formula_48 However the intersection of their projections need not be trivial.