Half-flat structures on decomposable Lie groups

2010/12/31 by Marco Freibert, Fabian Schulte-Hengesbach · 1 citation
Mathematics · #math.DG #msc:53C25 #msc:53C15 #msc:53C30

paper · pdf

published as Transform. Groups 17 (2012), no.1, 123-141 · 15 pages, v2: minor corrections and improved presentation

arxiv created 2012/03/15 · arxiv updated 2012/03/16

Abstract

Half-flat SU(3)-structures are the natural initial values for Hitchin's evolution equations whose solutions define parallel G₂-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.

Citations

• Half-flat structures on products of three-dimensional Lie groups

Cited by

• Half-flat structures on indecomposable Lie groups