Canonical Foliations of Certain Classes of Almost Contact Metric Structures

The purpose of this paper is to study the canonical foliations of an almost cosymplectic or almost Kenmotsu manifold M in a unified way. We prove that the canonical foliation defined by the contact distribution is Riemannian and tangentially almost Khler of codimension 1 and that is tangentially Khler if the manifold M is normal. Furthermore, we show that a semiinvariant submanifold N of such a manifold M admits a canonical foliation N which is defined by the antiinvariant distribution and a canonical cohomology class c(N) generated by a transversal volume form for N . In addition, we investigate the conditions when the evendimensional cohomology classes of N are nontrivial. Finally, we compute the GodbillonVey class for N .