论文标题
均匀球的不变纺纱器
Invariant Spinors on Homogeneous Spheres
论文作者
论文摘要
利用旋转表示以外部形式的表征，我们在Sphere $ s^n $的9个同质实现上对不变的旋转器进行了完整分类。在每种情况下，我们都会确定此类纺纱器空间的维度，给出其明确的描述，并根据度量研究基本相关的几何结构。我们在Sasaki和3-Sasaki案件中恢复了一些已知的结果，并找到了几个新示例：特别是我们给出了第一个已知的广义杀戮纺纱镜的示例，该例子具有四个不同的特征值。
Using the characterization of the spin representation in terms of exterior forms, we give a complete classification of invariant spinors on the nine homogeneous realizations of the sphere $S^n$. In each of the cases we determine the dimension of the space of such spinors, give their explicit description, and study the underlying related geometric structures depending on the metric. We recover some known results in the Sasaki and 3-Sasaki cases and find several new examples: in particular we give the first known examples of generalized Killing spinors with four distinct eigenvalues.
