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

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 $(\omega ,\varphi )$ of stable 2- and 3-forms with $d\varphi =\lambda {\omega }^2$ for some $\lambda \in \mathbb{R}\setminus \{0\}$.