In such complexes if in plane field
strength is greater than the out of the plane of field strength, [D.sub.1] will be positive and [sup.3][E.sub.g] level of [sup.3][T.sub.2g] will be lower than [sup.3][B.sub.2g] level whereas, if the out of plane field
strength is greater, [D.sub.1] will be negative and [sup.3][B.sub.2g] will be lower.
(Higher self intersection classes) Given A [subset] F as above one can take B to be a generic displacement of A (which will be r-atomic for all relevant r) and compute the "higher self intersections" of the plane field. Consider, for example, the complex line field [lambda] [subset] T[P.sup.3] on complex projective 3-space which is tangent to the fibres of the twistor map [P.sup.3] [right arrow] [S.sup.4].
These will include: Thom-Porteous formulas at the level of forms and currents, formulas of Poincare-Lelong type between Chern/Pontrjagin forms and linear dependency currents of families of cross-sections of a bundle, residue theorems relating degeneracies of maps between manifolds and characteristic forms, residue theorems for singularities of CR-structures, new invariants for pairs of complex structures, invariants for pairs of plane fields, higher self-intersection formulas for tangent plane fields, higher order contact currents for pairs of foliations and relations to characteristic forms.