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 R...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.展开更多
文摘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.
