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 S1. If the curvature transformation of the metric
associated with an almost cosymplectic space M commutes with the fundamental
singular collineation ϕ of M, then the related almost contact structure on M gives
rise to a complex structure on M ×R. The manifold M is then a cosymplectic space,
examples being given by taking the direct product of a Kaehler manifold with R or
S1. In particular, an almost cosymplectic manifold is cosymplectic if and only if it is
locally flat.
