Conformally parallel G_2 structures on a class of solvmanifolds
Differential Geometry
2012-06-19 v1 High Energy Physics - Theory
Abstract
Starting from a 6-dimensional nilpotent Lie group N endowed with an invariant SU(3) structure, we construct a homogeneous conformally parallel G_2-metric on an associated solvmanifold. We classify all half-flat SU(3) structures that endow the rank-one solvable extension of N with a conformally parallel G_2 structure. By suitably deforming the SU(3) structures obtained, we are able to describe the corresponding non-homogeneous Ricci-flat metrics with holonomy contained in G_2. In the process we also find a new metric with exceptional holonomy.
Keywords
Cite
@article{arxiv.math/0409137,
title = {Conformally parallel G_2 structures on a class of solvmanifolds},
author = {Simon G. Chiossi and Anna Fino},
journal= {arXiv preprint arXiv:math/0409137},
year = {2012}
}
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22 pages