Half-flat structures on decomposable Lie groups

Details Half-flat structures on decomposable Lie groups Half-flat structures on decomposable Lie groups

2010-12-16

arxiv.org/abs/1012.3714v2

Transform. Groups 17 (2012), no.1, 123-141

Mathematics

Differential Geometry

15 pages, v2: minor corrections and improved presentation

Scientific paper

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.

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