论文标题
挤压3-撒萨基人歧管的协会子曼菲尔德
Associative Submanifolds of Squashed 3-Sasakian Manifolds
论文作者
论文摘要
每一个紧凑的3-撒崎7个Manifold $ m $ $都承认一个规范的2参数$ \ text {g} _2 $ - 结构$ a，b> 0 $的$φ_{a，b} $ 4-孔。我们证明，由$（m，φ_{a，b}）$统治的3倍，与某种类型的大地测量相关，与几乎complex $ z \ z \ z \ z \ times s^2 $的伪旋构曲线相关，其中$ z $是$ x $ x $ x $ x $的结构。作为一种应用，我们在壁板7秒$（s^7，φ_{a，b}）$中构建了无限多种拓扑类型的非平凡的，紧凑的联想3倍，并挤压了异常的aloff-wallach空间$（n_ {1,1}，φ__{a，a，b}）$。从拓扑上讲，我们的示例是$ g $表面上的圆形捆绑包，对于任何$ g \ geq 0 $。
Every compact 3-Sasakian 7-manifold $M$ admits a canonical 2-parameter family of co-closed $\text{G}_2$-structures $φ_{a,b}$ for $a,b > 0$, as well as a foliation by $φ_{a,b}$-associative 3-folds whose leaf space $X$ is a positive quaternion-Kähler 4-orbifold. We prove that associative 3-folds in $(M,φ_{a,b})$ that are ruled by a certain type of geodesic are in correspondence with pseudo-holomorphic curves in the almost-complex 8-manifold $Z \times S^2$, where $Z$ is the twistor space of $X$ equipped with its strict nearly-Kähler structure. As an application, we construct infinitely many topological types of non-trivial, compact associative 3-folds in the squashed 7-spheres $(S^7, φ_{a,b})$ and squashed exceptional Aloff-Wallach spaces $(N_{1,1}, φ_{a,b})$. Topologically, our examples are circle bundles over a genus $g$ surface, for any $g \geq 0$.
