论文标题
$ \ text {su}（2）（2）^2 $ -Invariant cohoMOMOMOMOMOMOMOMOMOMONITY ONE MAIROLDS上的Coclosed $ g_2 $ - 结构
Coclosed $G_2$-structures on $\text{SU}(2)^2$-invariant cohomogeneity one manifolds
论文作者
论文摘要
我们考虑两个不同的$ \ text {su}（2）^2 $ -Invariant cohomogenity一个流形，一个非压缩$ m = \ mathbb {r}^4 \ times s^3 $和一个compact $ m = s^4 \ s^4 \ times s^3 $ $ g_2 $ - 结构是由半翼$ \ text {su}（3）$ - 结构构建的。对于$ \ mathbb {r}^4 \ times s^3 $，我们证明存在一个共锁定（但不一定是无扭转）$ g_2 $结构的家族，该结构由三个平滑函数提供，满足周围的某些边界条件，围绕单个轨道和非零参数。此外，该家族中的任何Coclosed $ g_2 $ - 结构构建。对于$ s^4 \ times s^3 $，我们证明没有$ \ text {su}（2）^2 $ -Invariant coclosed $ g_2 $ - 结构，该结构是由half half flat $ \ text {su}（su}（su}（3）$的结构）的结构。
We consider two different $\text{SU}(2)^2$-invariant cohomogeneity one manifolds, one non-compact $M=\mathbb{R}^4 \times S^3$ and one compact $M=S^4 \times S^3$, and study the existence of coclosed $\text{SU}(2)^2$-invariant $G_2$-structures constructed from half-flat $\text{SU}(3)$-structures. For $\mathbb{R}^4 \times S^3$, we prove the existence of a family of coclosed (but not necessarily torsion-free) $G_2$-structures which is given by three smooth functions satisfying certain boundary conditions around the singular orbit and a non-zero parameter. Moreover, any coclosed $G_2$-structure constructed from a half-flat $\text{SU}(3)$-structure is in this family. For $S^4 \times S^3$, we prove that there are no $\text{SU}(2)^2$-invariant coclosed $G_2$-structures constructed from half-flat $\text{SU}(3)$-structures.
