Invariant Generalized Almost Complex Structures on Real Flag Manifolds.

We characterize those real flag manifolds that can be endowed with invariant generalized almost complex structures. We show that no G M 2 -maximal real flag manifolds admit integrable invariant generalized almost complex structures. We give a concrete description of the generalized complex geometry on the maximal real flags of type B 2 , G 2 , A 3 , and D l with l ≥ 5 , where we prove that the space of invariant generalized almost complex structures under invariant B-transformations is homotopy equivalent to a torus and we classify all invariant generalized almost Hermitian structures on them. [ABSTRACT FROM AUTHOR]