Integrability of almost cosymplectic structures
Samuel I. Goldberg, Kentaro Yano · Pacific Journal of Mathematics · 1969
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 ό 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.5.