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arXiv · 1708.09119

Torsion-free $G_2$-structures with identical Riemannian metric

Christopher Lin
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Abstract

Based on a general formula due to R.Bryant, we work out the topological structure of the space of torsion-free $G_2$-structures generating the same associated Riemannian metric on a compact $7$-manifold. We also identify a corresponding Lie group-theoretic structure of the space. These observations are then used to describe the moduli space of torsion-free $G_2$-structures in certain cases - by way of covering spaces.

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Christopher Lin. 2017-08-30. Torsion-free $G_2$-structures with identical Riemannian metric. https://doi.org/10.1142/s1793525318500310

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