From complex contact structures to real almost contact 3-structures

Abstract

We prove that every complex contact structure gives rise to a distinguished type of almost contact metric 3-structure. As an application, 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 the well-known examples of contact circles defined by the Liouville-Cartan forms on the unit cotangent bundle of Riemann surfaces. Further, we provide sufficient conditions for a compact complex contact manifold to be the twistor space of a positive quaternionic Kähler manifold.