Lifting SU(3)-structures to nearly parallel G2-structures

Hitchin shows in [N. Hitchin, The geometry of three-forms in six and seven dimensions, J. Differ. Geom. 55 (2000) 547-576. math.DG/0010054v1; N. Hitchin, Stable forms and special metrics, Global Differential Geometry: The Mathematical Legacy of Alfred Gray, in: Contemp. Math., volume 288, American Math. Soc., 2001, pp. 70-89. math.DG/0107101v1] that half-flat SU(3)-structures on a six-dimensional manifold M can be lifted to parallel G2-structure on the product M×R. We show that Hitchin's approach can also be used to construct nearly parallel G2-structures by lifting so-called nearly half-flat structures. These SU(3)-structures are described by pairs (ω,φ) of stable 2- and 3-forms with dφ=λω2, for some λ∈R∖{0}.