1210.0953 (Haojie Chen et al.)

Generalized complex structures and almost bihermitian structures    [PDF]

Haojie Chen, Xiaolan Nie

Given an almost generalized complex structure, there exist associated almost bihermitian structures. We then derive geometric conditions for the integrability of an almost generalized complex structure in terms of its underlying almost bihermitian structures. As an application, we prove that a compact smooth 4-manifold has generalized complex structures of odd type if and only if it admits transversely holomorphic 2-foliations. Particularly, such structures exist on $S^1\times N^3$ for any compact 3-manifold $N^3$ with transversely holomorphic flow.

View original: http://arxiv.org/abs/1210.0953