Symplectic twistor spaces

The paper describes the geometry of the bundle T (M, ω) of the compatible complex structures of the tangent spaces of an (almost) symplectic manifold (M, ω), from the viewpoint of general twistor spaces [3], [9], [1]. It is shown that M has an either complex or almost Kaehler twistor space iff it has a flat symplectic connection. Applications of the twistor space T to the study of the differential forms of M, and to the study of mappings φ{symbol}: N → M, where N is a Kaehler manifold are indicated.