How to construct all metric $f$-$K$-contact manifolds

TL;DR

This paper demonstrates that all compact metric f-K-contact and S-manifolds can be constructed from known structures using specific geometric operations like mapping tori, rotations, and deformations.

Contribution

It provides a systematic method to generate all such manifolds from existing K-contact and Sasakian manifolds through iterative geometric constructions.

Findings

All compact metric f-K-contact manifolds derive from K-contact manifolds.

All compact metric S-manifolds derive from Sasakian manifolds.

Construction involves mapping tori, rotations, and type II deformations.

Abstract

We show that any compact metric $f$-$K$-contact, respectively $S$-manifold is obtained from a compact $K$-contact, respectively Sasakian manifold by an iteration of constructions of mapping tori, rotations, and type II deformations.