Torsion-free $G_2$-structures with identical Riemannian metric
Differential Geometry
2017-08-31 v1
Abstract
Based on a general formula due to R.Bryant, we work out the topological structure of the space of torsion-free -structures generating the same associated Riemannian metric on a compact -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 -structures in certain cases - by way of covering spaces.
Keywords
Cite
@article{arxiv.1708.09119,
title = {Torsion-free $G_2$-structures with identical Riemannian metric},
author = {Christopher Lin},
journal= {arXiv preprint arXiv:1708.09119},
year = {2017}
}
Comments
18 pages, to appear in Journal of Topology and Analysis (2018) - accepted May 9, 2017. Some results overlap with arXiv:1510.04226