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arXiv · 2212.01812

The Space of Closed $G_2$-Structures. I. Connections

Pengfei Xu·Kai Zheng
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Abstract

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.

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Pengfei Xu, Kai Zheng. 2022-12-04. The Space of Closed $G_2$-Structures. I. Connections. https://doi.org/10.1093/qmath%2Fhaae004

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