English

Sewing cells in almost cosymplectic and almost Kenmotsu geometry

Differential Geometry 2012-04-02 v2

Abstract

For a finite family of 3-dimensional almost contact metric manifolds with closed the structure form η\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 α\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.

Keywords

Cite

@article{arxiv.1203.4778,
  title  = {Sewing cells in almost cosymplectic and almost Kenmotsu geometry},
  author = {Piotr Dacko},
  journal= {arXiv preprint arXiv:1203.4778},
  year   = {2012}
}

Comments

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