Sewing cells in almost cosymplectic and almost Kenmotsu geometry

Abstract

For a finite family of 3-dimensional almost contact metric manifolds with closed the structure form $\eta$ is described a construction of an almost contact metric manifold, where the members of the family are building blocks - cells. Obtained manifold share many properties of cells. One of the more important are nullity conditions. If cells satisfy nullity conditions - then - in the case of almost cosymplectic or almost $\alpha$-Kenmotsu manifolds - "sewed cells" also satisfies nullity condition - but generally with different constants. It is important that even in the case of the generalized nullity conditions - "sewed cells" are the manifolds which satisfy such conditions provided the cells satisfy the generalized nullity conditions.

minor corrections, changed the proof of the Proposition 1 from the preliminary part