G2-structure deformations and warped products
Differential Geometry
2013-01-22 v2
Abstract
We overview the properties of non-infinitesimal deformations of G2-structures on seven-manifolds, and in particular, focus on deformations that lie in the seven-dimensional representation of G2 and are thus defined by a vector. We then consider deformations from G2-structures with the torsion class having one-dimensional and seven-dimensional components (so-called conformally nearly parallel G2-manifolds) to G2-structures with just a one-dimensional torsion component (nearly parallel G2-manifolds). We find that deformations between such structures exist if and only if the metric is a particular warped product metric.
Cite
@article{arxiv.1110.4594,
title = {G2-structure deformations and warped products},
author = {Sergey Grigorian},
journal= {arXiv preprint arXiv:1110.4594},
year = {2013}
}
Comments
13 pages, v2 - corrected typos, clarified proof of Thm 4.4, updated references