Lifting SU(3)-structures to nearly parallel G_{2}-structures

Details Lifting SU(3)-structures to nearly parallel G_{2}-structures Lifting SU(3)-structures to nearly parallel G_{2}-structures

2007-07-13

arxiv.org/abs/0707.2029v1

Mathematics

Differential Geometry

10 pages

Scientific paper

Hitchin shows that half-flat SU(3)-structures on a 6-dimensional manifold M can be lifted to parallel G_{2}-structure on the product $M\times\mathbb{R}$. We show that Hitchin's approach can also be used to construct nearly parallel G_{2}-structures by lifting so-called nearly half-flat structures. These SU(3)-structures are described by pairs $(\omega,\phi)$ of stable 2- and 3-forms with $d\phi=\lambda\omega^{2}$ for some $\lambda\in\mathbb{R}\setminus\{0\}$.

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