论文标题
五维触点几何形状中的纺纱器
Spinors in Five-Dimensional Contact Geometry
论文作者
论文摘要
我们使用经典（Penrose）的两个组分旋转器在五个维度上建立了两个抛物线接触结构的差分几何形状，即$ G_2 $接触几何和legendrean接触几何形状。这两个几何形状中的主要参与者是仅在触点方向上定义的定义定义的定义衍生物。我们解释了如何定义它们及其在构建基本不变的诸如谐波曲率之类的基本不变性方面的用法，从抛物线观点来看，障碍物是局部平坦的障碍。作为应用程序，我们计算了飞碟的配置空间上$ G_2 $接触结构的不变扭转（始终是五维触点歧管）。
We use classical (Penrose) two-component spinors to set up the differential geometry of two parabolic contact structures in five dimensions, namely $G_2$ contact geometry and Legendrean contact geometry. The key players in these two geometries are invariantly defined directional derivatives defined only in the contact directions. We explain how to define them and their usage in constructing basic invariants such as the harmonic curvature, the obstruction to being locally flat from the parabolic viewpoint. As an application, we calculate the invariant torsion of the $G_2$ contact structure on the configuration space of a flying saucer (always a five-dimensional contact manifold).
