标题： 7维中的$G_2$结构的模空间与Strominger系统 显示英文标题

标题： Moduli of $G_2$ structures and the Strominger system in dimension 7

摘要： 我们考虑在紧致的$7$维流形上与$G_2$-瞬子耦合的带有挠率的$G_2$结构。 这种耦合通过超引力和广义几何中出现的一个关于$4$-形式的方程实现，该方程被称为比安基恒等式。 由此产生的偏微分方程组可以看作是$7$维数下Strominger系统的类比。 我们开始研究解的模空间，并利用椭圆算子理论证明其为有限维。 我们还讨论了相关的几何结构与广义几何之间的联系。 显示英文摘要

摘要： We consider $G_2$ structures with torsion coupled with $G_2$-instantons, on a compact $7$-dimensional manifold. The coupling is via an equation for $4$-forms which appears in supergravity and generalized geometry, known as the Bianchi identity. The resulting system of partial differential equations can be regarded as an analogue of the Strominger system in $7$-dimensions. We initiate the study of the moduli space of solutions and show that it is finite dimensional using elliptic operator theory. We also relate the associated geometric structures to generalized geometry.