论文标题
几乎是平行的$ g_2 $ -manifolds：形式和关联子曼佛群岛
Nearly parallel $G_2$-manifolds: formality and associative submanifolds
论文作者
论文摘要
我们构建了简单连接的紧凑型SasakiEinstein 7-manifolds的新例子。我们确定了$ CP^2 $的任何光纤束的总空间的最小模型，带有纤维$ s^1 \ times s^2 $或$ s^3/z_p $（$ p> 0 $），我们将其应用于Aloff-Wallach空间是正式的。我们还找到了形式流形和非正式流形的示例，它们是局部共形的平行$ spin（7）$ - 歧管。 另一方面，我们在Aloff-Wallach空间以及任何常规的Sasaki-Einstein 7-Manifold中构建了关联最小的子曼佛。特别是，在空间中，$ q（1,1,1）=（su（2）\ times su（2）\ times su（2））/（u（1）\ times u（1）u（1））$，其自然$ s^1 $ - 几乎是平行$ g_2 $结构的sasaki-iinstein结构引起的$ g_2 $结构。在每种情况下，我们都会获得一个非平凡关联变形的家族。
We construct new examples of non-formal simply connected compact Sasaki-Einstein 7-manifolds. We determine the minimal model of the total space of any fibre bundle over $CP^2$ with fibre $S^1\times S^2$ or $S^3/Z_p$ ($p>0$), and we apply this to conclude that the Aloff-Wallach spaces are formal. We also find examples of formal manifolds and non-formal manifolds, which are locally conformal parallel $Spin(7)$-manifolds. On the other hand, we construct associative minimal submanifolds in the Aloff-Wallach spaces and in any regular Sasaki-Einstein 7-manifold; in particular, in the space $Q(1,1,1)=(SU(2) \times SU(2) \times SU(2))/ (U(1) \times U(1))$ with the natural $S^1$-family of nearly parallel $G_2$-structures induced by the Sasaki-Einstein structure. In each of those cases, we obtain a family of non-trivial associative deformations.
