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Bibliographic Details
Main Authors: Xu, Pengfei, Zheng, Kai
Format: Preprint
Published: 2022
Subjects:
Online Access:https://arxiv.org/abs/2212.01812
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Table of Contents:
  • 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.