 Thesefore if formula_22 and formula_33 are sections of formula_1 then

and so formula_20 is isotropic.Furthermore, formula_20 is maximal because there are formula_38 (complex) dimensions of choices for formula_39 and formula_18 is unrestricted on the complement of formula_41 which is of (complex) dimension formula_42 Thus the total (complex) dimension in "n".Gualtieri has proven that all maximal isotropic subbundles are of the form formula_20 for some formula_44 and formula_45

The type of a maximal isotropic subbundle formula_20 is the real dimension of the subbundle that annihilates E. Equivalently it is 2"N" minus the real dimension of the projection of formula_20 onto the tangent bundle T. In other words, the type of a maximal isotropic subbundle is the codimension of its projection onto the tangent bundle.