Half-flat structures on indecomposable Lie groups

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

2011-10-07

arxiv.org/abs/1110.1512v2

Mathematics

Differential Geometry

25 pages, v2: minor corrections due to the new classification of the six-dimensional Lie algebras with five-dimensional nilrad

Scientific paper

This article can be viewed as a continuation of the articles arXiv:0912.3486 and arXiv:1012.3714 where the decomposable Lie algebras admitting half-flat SU(3)-structures are classified. The new main result is the classification of the indecomposable six-dimensional Lie algebras with five-dimensional nilradical which admit a half-flat SU(3)-structure. As an important step of the proof, a considerable refinement of the classification of six-dimensional Lie algebras with five-dimensional non-Abelian nilradical is established. Additionally, it is proved that all non-solvable six-dimensional Lie algebras admit half-flat SU(3)-structures.

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