From complex contact structures to real almost contact 3-structures

TL;DR

This paper establishes a link between complex contact structures and almost contact 3-structures, providing new examples of manifolds with special geometric structures and insights into their relation to quaternionic Kähler and Fano contact manifolds.

Contribution

It proves that complex contact structures induce almost contact metric 3-structures and offers new examples and conditions relating to quaternionic Kähler and Fano contact manifolds.

Findings

Construction of new manifold examples with special structures

Conditions for complex contact manifolds to be twistor spaces

Evidence supporting the LeBrun-Salamon conjecture

Abstract

In this work, we prove that every complex contact structure gives rise to a distinguished type of almost contact metric 3-structure. As an application of our main result, we provide several new examples of manifolds which admit taut contact circles, taut and round almost cosymplectic 2-spheres, and almost hypercontact (metric) structures. These examples generalize, in a suitable sense, the well-known examples of contact circles defined by the Liouville-Cartan forms on the unit cotangent bundle of Riemann surfaces. Furthermore, we provide sufficient conditions for a compact complex contact manifold to be the twistor space of a positive quaternionic K\"{a}hler manifold. In the particular setting of Fano contact manifolds, from our main result, we also obtain new evidences supporting the LeBrun-Salamon conjecture.