We observe that the class of metric $f$-$K$-contact manifolds, which naturally contains that of $K$-contact manifolds, is closed under forming mapping tori of automorphisms of the structure. We show that the de Rham cohomology of compact metric $f$-$K$-contact manifolds naturally splits off an exterior algebra, and relate the closed leaves of the characteristic foliation to its basic cohomology.

中文翻译：

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关于度量 f-K 接触流形的拓扑结构

我们观察到度量 $f$-$K$-contact 流形的类，自然包含 $K$-contact 流形的类，在形成结构的自同构映射环下是封闭的。我们展示了紧凑度量 $f$-$K$-contact 流形的 de Rham 上同调自然地从外部代数中分离出来，并将特征叶面的闭合叶子与其基本上同调联系起来。