A non-Sasakian Lefschetz K-contact manifold of Tievsky type

TL;DR

This paper introduces a new family of five-dimensional compact manifolds that are K-contact and satisfy the Hard Lefschetz Theorem, sharing properties with Sasakian manifolds but lacking a Sasakian structure.

Contribution

It provides the first examples of non-Sasakian K-contact manifolds of Tievsky type that fulfill the Hard Lefschetz Theorem.

Findings

Existence of five-dimensional K-contact manifolds satisfying Hard Lefschetz

These manifolds have Tievsky type models similar to Sasakian manifolds

They do not admit any Sasakian structure

Abstract

We find a family of five dimensional completely solvable compact manifolds that constitute the first examples of $K$-contact manifolds which satisfy the Hard Lefschetz Theorem and have a model of Tievsky type just as Sasakian manifolds but do not admit any Sasakian structure.