Generalized Sasakian-space-forms are introduced and studied. Many examples of these manifolds are presented, by using some different geometric techniques such as Riemannian submersions, warped products or conformal and related transformations. New results on generalized complex-space-forms are also obtained.

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Generalized Sasakian-space-forms

In this paper, we completely characterize the local structure of trans-Sasakian manifolds of dimension ⩾ 5 by giving suitable examples.

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The local structure of trans-Sasakian manifolds

It is obtained a complete classification for almost contact metric manifolds through the study of the covariant derivative of the fundamental 2- form on those manifolds.

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A classification of almost contact metric manifolds

This paper studies conformal and related changes of the product metric on the product of two almost contact metric manifolds. It is shown that if one factor is Sasakian, the other is not, but that locally the second factor is of the type studied by Kenmotsu. The results are more general and given in terms of trans-Sasakian, a-Sasakian and s-Kenmotsu structures.

Conformal and related changes of metric on the product of two almost contact metric manifolds

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.

Canonical Foliations of Certain Classes of Almost Contact Metric Structures

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Dirk Janssens

Papers

Almost contact structures and curvature tensors