# On the topology of metric $f$-$K$-contact manifolds

## TL;DR

This paper studies the structure and cohomology of metric $f$-$K$-contact manifolds, showing their stability under certain constructions and revealing their cohomological decomposition and foliation properties.

## Contribution

It introduces the class of metric $f$-$K$-contact manifolds, proves their closure under mapping tori, and describes their de Rham cohomology and foliation characteristics.

## Key findings

- Metric $f$-$K$-contact manifolds are closed under mapping tori construction.
- Their de Rham cohomology splits off an exterior algebra.
- Closed leaves of the characteristic foliation relate to basic cohomology.

## Abstract

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.