Local models and integrability of certain almost Kahler 4-manifolds

Apostolov, Vestislav; Armstrong, John; Draghici, Tedi

Local models and integrability of certain almost Kahler 4-manifolds

Authors

Apostolov, Vestislav

Armstrong, John

Draghici, Tedi

Description

We classify, up to a local isometry, all non-Kahler almost Kahler 4-manifolds for which the fundamental 2-form is an eigenform of the Weyl tensor, and whose Ricci tensor is invariant with respect to the almost complex structure. Equivalently, such almost Kahler 4-manifolds satisfy the third curvature condition of A. Gray. We use our local classification to show that, in the compact case, the third curvature condition of Gray is equivalent to the integrability of the corresponding almost complex structure.
25 pages, final version, accepted in Math. Annalen