论文标题
几乎$ \ mathrm {g} _2 $歧管的变形理论
Deformation theory of nearly $\mathrm{G}_2$ manifolds
论文作者
论文摘要
我们研究了几乎$ \ mathrm {g} _2 $歧管的变形理论。这是承认真正的杀戮旋转器的七个维歧管。我们表明，几乎$ \ mathrm {g} _2 $结构的无限变形总体上被阻塞。明确地，我们证明了均质的几乎$ \ mathrm {g} _2 $结构的无限变形 - 瓦拉奇空间都被阻塞到二阶。我们还完全描述了几乎$ \ mathrm {g} _2 $歧管的共同体。
We study the deformation theory of nearly $\mathrm{G}_2$ manifolds. These are seven dimensional manifolds admitting real Killing spinors. We show that the infinitesimal deformations of nearly $\mathrm{G}_2$ structures are obstructed in general. Explicitly, we prove that the infinitesimal deformations of the homogeneous nearly $\mathrm{G}_2$ structure on the Aloff--Wallach space are all obstructed to second order. We also completely describe the cohomology of nearly $\mathrm{G}_2$ manifolds.
