论文标题
在几乎平行的$ \ mathrm {g} _2 $ -Manifolds上杀死旋转器的无限变形
Infinitesimal deformations of Killing spinors on nearly parallel $\mathrm{G}_2$-manifolds
论文作者
论文摘要
承认杀人纺纱器的歧管是爱因斯坦歧管。因此，杀死旋转器的变形需要爱因斯坦指标的变形。在本文中，我们研究了在几乎平行的$ \ mathrm {g} _2 $ -Manifolds上杀死旋转器的无限变形。由于几乎平行的$ \ mathrm {g} _2 $ - 结构与7维旋转歧管上的杀死纺纱器之间存在一对一的对应关系，因此我们的结果表明，在杀死纺纱器的情况下检查了几乎并行$ \ mathrm {g} _2 $结构的无限变形。采用相同的技术，我们确定Rarita-Schinginger田地的空间与Laplacian的特征空间的子空间一致。
Manifolds admitting Killing spinors are Einstein manifolds. Thus, a deformation of a Killing spinor entails a deformation of Einstein metrics. In this paper, we study infinitesimal deformations of Killing spinors on nearly parallel $\mathrm{G}_2$-manifolds. Since there is a one-to-one correspondence between nearly parallel $\mathrm{G}_2$-structures and Killing spinors on 7-dimensional spin manifolds, our results imply that infinitesimal deformations of nearly parallel $\mathrm{G}_2$-structures are examined in terms of Killing spinors. Applying the same technique, we identify that the space of the Rarita-Schwinger fields coincides with a subspace of the eigenspace of the Laplacian.
