论文标题
从复杂的接触结构到实际几乎接触3结构
From complex contact structures to real almost contact 3-structures
论文作者
论文摘要
在这项工作中，我们证明每个复杂的接触结构都会产生几乎接触度量的杰出类型。作为我们的主要结果的应用，我们提供了几个新的歧管示例，这些示例允许绷紧的接触圆，绷紧和几乎偶然的2杆圆形和几乎超触及（公制）结构。这些示例从适当的意义上概括了由liouville-cartan形式定义的众所周知的接触圆的例子，该单位cotangent bundle bundle是riemann表面的。此外，我们为紧凑的复杂接触歧管提供了足够的条件，使其成为阳性QuaternionicKähler歧管的扭曲器空间。从我们的主要结果来看，在Fano接触歧管的特定设置中，我们还获得了支持Lebrun-Salamon猜想的新证据。
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 Kähler manifold. In the particular setting of Fano contact manifolds, from our main result, we also obtain new evidences supporting the LeBrun-Salamon conjecture.
