论文标题
通过动力学系统旋转（7）载体的几何过渡
Geometric transitions with Spin(7) holonomy via a dynamical system
论文作者
论文摘要
我们阐明了两个1参数族的共同体家族的全球几何形状，一个旋转（7）具有通用轨道的自动衡量标准与Aloff-aloft-wallach-wallach space $ n（1，-1，-1）\ cong \ mathrm {surm {su}（su}（3）/\ mathrm {u}（u}（1）$ singular orbits $ sitular of po $由Reidegeld证明存在。这两个家族适合以前已知的共同体族的地理位置，具有特殊的人工学指标，并在Calabi-Yau 3倍的情况下提供了众所周知的Conifold过渡的旋转（7）类似物。此外，我们发现，旋转（7）固体指标的家族存在另一个过渡，一端具有类似的渐近行为，但另一端是单数。我们通过将自旋（7） - 方程与3维立方体上的简单动力学系统相关联获得结果。
We clarify the global geometry of two 1-parameter families of cohomogeneity one Spin(7) holonomy metrics with generic orbit the Aloff--Wallach space $N(1,-1) \cong \mathrm{SU}(3)/\mathrm{U}(1)$ and singular orbits $S^5$ and $\mathbb{C}P^2$, which at short distance were shown to exist by Reidegeld. The two families fit into the geography of previously known families of cohomogeneity one metrics with exceptional holonomy and provide a Spin(7) analogue of the well-known conifold transition in the setting of Calabi--Yau 3-folds. Furthermore, we discover that there is another transition to families of Spin(7) holonomy metrics which have a similar asymptotic behaviour on one end, but are singular on the other end. We obtain our results by relating the Spin(7)-equations to a simple dynamical system on a 3-dimensional cube.
