Integrability of almost cosymplectic structures

Integrability conditions for almost cosymplectic structures on almost contact manifolds are obtained. Examples of these structures are given by taking the direct product of an almost Kaehler manifold with a line R or a circle S 1 . If the curvature transformation of the metric associated with an almost cosymplectic space M commutes with the fundamental singular collineation of M, then the related almost contact structure on M gives rise to a complex structure on M X R. The manifold M is then a cosymplectic space, examples being given by taking the direct product of a Kaehler manifold with R or S 1 . In particular, an almost cosymplectic manifold is cosymplectic if and only if it is locally flat.