Odd type generalized complex structures on 4-manifolds
  We prove that a compact smooth 4-manifold admits generalized complex structures of odd type if and only if it has a transversely holomorphic 2-foliation. Consequently, there exist generalized complex structures of odd type on a circle bundle over a closed Seifert fibered 3-manifold. 
Haojie Chen, Xiaolan Nie
math.DG math-ph math.MP