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arXiv · 2009.10797

From complex contact structures to real almost contact 3-structures

Eder M. Correa
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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.

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Eder M. Correa. 2020-09-22. From complex contact structures to real almost contact 3-structures. https://arxiv.org/abs/2009.10797

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