论文标题
关闭$ G_2 $ - 结构的空间。 I.连接
The Space of Closed $G_2$-Structures. I. Connections
论文作者
论文摘要
在本文中，我们开发了针对给定同胞类中封闭$ g_2 $结构空间的几何理论的基础理论，作为无限二维流形。我们介绍Sobolev型指标，构建其Levi-Civita连接，制定地球方程，并分析这些Sobolev-type指标下的Torsion Free $ G_2 $结构的变化结构。
In this article, we develop foundational theory for geometries of the space of closed $G_2$-structures in a given cohomology class as an infinite-dimensional manifold. We introduce Sobolev-type metrics, construct their Levi-Civita connections, formulate geodesic equations, and analyse the variational structures of torsion free $G_2$-structures under these Sobolev-type metrics.
