论文标题
关于精确g $ _ {2} $的备注 - 紧凑型歧管上的结构
Remarks on Exact G$_{2}$-Structures on Compact Manifolds
论文作者
论文摘要
g $ _ {2} $几何形状中的一个重要的开放问题是涉及紧凑的七个manifold是否可以支持精确的g $ _ {2} $ - 结构。鉴于此问题的重要性，我们启动了精确的G $ _ {2} $ - 紧凑型歧管上的结构。我们专注于确切的G $ _2 $ - 结构，但我们也没有其他约束，但是我们还考虑了封闭的G $ _ {2} $的确切条件与其他条件之间的关系 - 例如极端的Ricci pincheded和Laplacian Soliton条件。
An important open question in G$_{2}$ geometry concerns whether or not a compact seven-manifold can support an exact G$_{2}$-Structure. Given the significance of this question we initiate a study of exact G$_{2}$-Structures on compact manifolds. We focus on exact G$_2$-Structures subject to no additional constraints but we also consider the relationship between the exact condition and other conditions for closed G$_{2}$-Structures such as the Extremally Ricci-Pinched and Laplacian Soliton conditions.
