Cocalibrated G_2-structures on products of four- and three-dimensional Lie groups

Details Cocalibrated G_2-structures on products of four- and three-dimensional Lie groups Cocalibrated G_2-structures on products of four- and three-dimensional Lie groups

2012-03-30

arxiv.org/abs/1203.6858v1

Mathematics

Differential Geometry

33 pages

Scientific paper

Cocalibrated G_2-structures are structures naturally induced on hypersurfaces in Spin(7)-manifolds. Conversely, such structures can be used to construct Spin(7)-manifolds via the Hitchin flow. In this article, we concentrate as in arXiv:1109.4774 on left-invariant cocalibrated G_2-structures on Lie groups, but now on those Lie groups G which are a direct product G=G_4 \times G_3 of a four-dimensional Lie group G_4 and a three-dimensional Lie group G_3. We achieve a full classification of the Lie groups G=G_4 \times G_3 which admit such structures.

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