The Space of Closed G2-Structures. I. Connections
Abstract
In this article, we develop foundational theory for geometries of the space of closed G2-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 G2-structures under these Sobolev-type metrics.
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