论文标题
封闭$ \ text {sl}（3，\ mathbb {c}）$ - nilmanifolds上的结构
Closed $\text{SL}(3,\mathbb{C})$-structures on nilmanifolds
论文作者
论文摘要
在本文中，我们考虑关闭的$ \ text {sl}（3，\ mathbb {c}）$ - 结构是平均凸或通过符号形式驯服的结构。这些概念是由唐纳森（Donaldson）引入的，与$ \ text {g} _2 $ -Manifolds具有边界。特别是，我们对携带不变的平均凸的Nilmanifolds进行了分类，$ \ text {sl}（3，\ mathbb {c}）$ - 结构和那些接纳不变的均值均值凸的半flat $ \ text {su} su}（su}（3）$ - 结构。我们还证明，如果一个solvmanifold承认不变的tamed tame tame oft $ \ text {sl}（3，\ mathbb {c}）$ - 结构，则它还具有不变的符号符号符号符号flat $ \ text {su}（su}（su}（3）$ - 结构。
In this paper we consider closed $\text{SL}(3,\mathbb{C})$-structures which are either mean convex or tamed by a symplectic form. These notions were introduced by Donaldson in relation to $\text{G}_2$-manifolds with boundary. In particular, we classify nilmanifolds which carry an invariant mean convex closed $\text{SL}(3,\mathbb{C})$-structure and those which admit an invariant mean convex half-flat $\text{SU}(3)$-structure. We also prove that, if a solvmanifold admits an invariant tamed closed $\text{SL}(3,\mathbb{C})$-structure, then it also has an invariant symplectic half-flat $\text{SU}(3)$-structure.
