Local models and integrability of certain almost Kahler 4-manifolds

Details Local models and integrability of certain almost Kahler 4-manifolds Local models and integrability of certain almost Kahler 4-manifolds

2001-09-15

arxiv.org/abs/math/0109098v2

Mathematics

Differential Geometry

25 pages, final version, accepted in Math. Annalen

Scientific paper

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.

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