Canonical Foliations of Certain Classes of Almost Contact Metric Structures
Canonical Foliations of Certain Classes of Almost Contact Metric Structures
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DOI：
10.1007/s10114-004-0520-2
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发表时间：
2005-06
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影响因子：
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通讯作者：
Tae Wan Kim;H. Pak
中科院分区：
文献类型：
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作者：
Tae Wan Kim;H. Pak
本文的目的是统一地研究几乎余辛流形或几乎Kenmotsu流形的标准叶理。证明了由接触分布定义的正则叶理是黎曼的且切向几乎余维为1的Kähler，且当流形M是正态的时，正则叶理是切向Kähler.此外，我们证明了这样的流形的一个半不变子流形N具有一个由反不变分布所定义的典型叶理N和一个由N的一个横截体积形式所生成的典型上同调类C（N）。此外，我们还研究了N的偶维上同调类非平凡的条件。最后，我们计算的Godbillon-Vey类的cBN。
The purpose of this paper is to study the canonical foliations of an almost cosymplectic or almost Kenmotsu manifoldMin a unified way. We prove that the canonical foliation ℱ defined by the contact distribution is Riemannian and tangentially almost Kähler of codimension 1 and that ℱ is tangentially Kähler if the manifoldMis normal. Furthermore, we show that a semi–invariant submanifoldNof such a manifoldMadmits a canonical foliation ℱNwhich is defined by the antiinvariant distribution and a canonical cohomology classc(N)generated by a transversal volume form for ℱN. In addition, we investigate the conditions when the even–dimensional cohomology classes ofNare non–trivial. Finally, we compute the Godbillon–Vey class for ℱN.