 its complex rank equals "N" and formula_11 for all formula_12

Vice versa, any subbundle "L" satisfying (i), (ii) is the formula_6-eigenbundle of a unique generalized almost complex structure, so that the properties (i), (ii) can be considered as an alternative definition of generalized almost complex structure.In ordinary complex geometry, an almost complex structure is integrable to a complex structure if and only if the Lie bracket of two sections of the holomorphic subbundle is another section of the holomorphic subbundle.In generalized complex geometry one is not interested in vector fields, but rather in the formal sums of vector fields and one-forms.