The curvature and the integrability of almost-Kahler manifolds: a survey

Abstract

We survey some recent results and constructions of almost-Kähler manifolds whose curvature tensors have certain algebraic symmetries. This is an updated and corrected version of the (to be) published manuscript.

30 pages, to appear in `Symplectic and Contact Topology: Interactions and Perspectives', (eds. Y.Eliashberg, B. Khesin, F. Lalonde), Fields Institute Communications Series, AMS, 2003