论文标题
旋转（7）Kähler几何形状的指标
Spin(7) metrics from Kähler Geometry
论文作者
论文摘要
我们调查了$ \ mathbb {t}^2 $ - torsion free $ spin（7）$ - $ 8 $ manifold上的torsion $ spin（7）$ - manifold的质量。我们表明，存在Hamiltonian $ S^1 $或$ \ MATHBB {T}^2 $ ACTION在保留复杂结构的商品上。在每种情况下，进行Kähler减少都会减少查找$ spin（7）$度量的问题，以研究$ 4 $ - 或$ 2 $ - manifold带有微不足道的规范捆绑包的PDE系统，在紧凑型情况下，该系统与$ \ Mathbb {t}^4 $，k3表面或Ellipt curve相对应。通过逆转这种结构，我们给出了许多新的明确示例$ spin（7）$自动指标。在最简单的情况下，我们的结果可以看作是吉本人 - 鹰安萨斯的扩展。
We investigate the $\mathbb{T}^2$-quotient of a torsion free $Spin(7)$-structure on an $8$-manifold under the assumption that the quotient $6$-manifold is Kähler. We show that there exists either a Hamiltonian $S^1$ or $\mathbb{T}^2$ action on the quotient preserving the complex structure. Performing a Kähler reduction in each case reduces the problem of finding $Spin(7)$ metrics to studying a system of PDEs on either a $4$- or $2$-manifold with trivial canonical bundle, which in the compact case corresponds to either $\mathbb{T}^4$, a K3 surface or an elliptic curve. By reversing this construction we give infinitely many new explicit examples of $Spin(7)$ holonomy metrics. In the simplest case, our result can be viewed as an extension of the Gibbons-Hawking ansatz.
