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

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

2009-12-17

arxiv.org/abs/0912.3486v1

J. Geom. Phys. 60 (2010), pp. 1726-1740

Mathematics

Differential Geometry

19 pages

Scientific paper

10.1016/j.geomphys.2010.06.012

We classify six-dimensional Lie groups which admit a left-invariant half-flat SU(3)-structure and which split in a direct product of three-dimensional factors. Moreover, a complete list of those direct products is obtained which admit a left-invariant half-flat SU(3)-structure such that the three-dimensional factors are orthogonal. Similar classification results are proved for left-invariant half-flat SL(3,R)-structures on direct products with either definite and orthogonal or isotropic factors.

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