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

Christopher Lin

doi:10.1142/S1793525318500310

paper

Torsion-free $G_{2}$ -structures with identical Riemannian metric

arXiv:1708.09119 · doi:10.1142/S1793525318500310

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.

18 pages, to appear in Journal of Topology and Analysis (2018) - accepted May 9, 2017. Some results overlap with arXiv:1510.04226

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Laplacian Solitons and Symmetry in G_2-geometry

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Torsion-free $G_{2}$ -structures with identical Riemannian metric