Abstract

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 ℱ defined by the contact distribution is Riemannian and tangentially almost Kahler of codimension 1 and that ℱ is tangentially Kahler if the manifold M is normal. Furthermore, we show that a semi–invariant submanifold N of such a manifold M admits a canonical foliation ℱN which is defined by the antiinvariant distribution and a canonical cohomology class c(N) generated by a transversal volume form for ℱN. In addition, we investigate the conditions when the even–dimensional cohomology classes of N are non–trivial. Finally, we compute the Godbillon–Vey class for ℱN.

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