Half-flat structures on decomposable Lie groups
Differential Geometry
2012-03-16 v2
Abstract
Half-flat SU(3)-structures are the natural initial values for Hitchin's evolution equations whose solutions define parallel G_2-structures. Together with the results of arXiv:0912.3486v1, the results of this article completely solve the existence problem of left-invariant half-flat SU(3)-structures on decomposable Lie groups. The proof is supported by the calculation of the Lie algebra cohomology for all indecomposable five-dimensional Lie algebras which refines and clarifies the existing classification of five-dimensional Lie algebras.
Keywords
Cite
@article{arxiv.1012.3714,
title = {Half-flat structures on decomposable Lie groups},
author = {Marco Freibert and Fabian Schulte-Hengesbach},
journal= {arXiv preprint arXiv:1012.3714},
year = {2012}
}
Comments
15 pages, v2: minor corrections and improved presentation