On simply connected K-contact non-Sasakian manifolds

TL;DR

This paper proves the existence of simply connected K-contact manifolds that do not admit Sasakian structures, using methods from contact and symplectic geometry, specifically the fat bundle technique.

Contribution

It provides a solution to a longstanding problem by constructing examples of simply connected K-contact manifolds without Sasakian structures.

Findings

Existence of simply connected K-contact non-Sasakian manifolds confirmed.

Application of fat bundle method from contact and symplectic geometry.

Advancement in understanding the relationship between K-contact and Sasakian geometries.

Abstract

We solve the problem posed by Boyer and Galicki about the existence of K-contact simply connected manifolds with no Sasakian structure. Although the result lies in the framework of metric contact geometry, our methods come from contact and symplectic geometry and are based on the method of fat bundles developed by Sternberg, Weinstein and Lerman.