论文标题
$ \ mathbb {r}^4 \ times s^3 $变形$ g_2 $ -instantons
Deformed $G_2$-instantons on $\mathbb{R}^4 \times S^3$
论文作者
论文摘要
我们在$ \ mathbb {r}^4 \ times s^3 $上构建了变形的$ g_2 $ -instantons的明确示例，也称为Donaldson-Thomas Connections。并在$ \ Mathbb {r}^+\ times s^3 \ times s^3 $赋予了布莱恩特 - 萨拉曼圆锥形$ g_2 $ - 结构。这些是$ G_2 $歧管上的第一个此类非平凡示例。作为我们调查的副产品，我们还找到了$ \ mathbb {r}^4 \ times s^3 $ by $ \ mathbb {r}^2 \ times s^1 $的关联叶子。
We construct explicit examples of deformed $G_2$-instantons, also called Donaldson-Thomas connections, on $\mathbb{R}^4 \times S^3$ endowed with the torsion free $G_2$-structure found by Brandhuber et al. and on $\mathbb{R}^+\times S^3 \times S^3$ endowed with the Bryant-Salamon conical $G_2$-structure. These are the first such non-trivial examples on a $G_2$ manifold. As a by-product of our investigation we also find an associative foliation of $\mathbb{R}^4\times S^3$ by $\mathbb{R}^2 \times S^1$.
